A Nationalist Spain has the further advantage (for Germany) or forcing the French to guard their south border (at least more than with a Communist / socialist / republican Spain).
Plus, once France is beaten, a Nationalist Spain MAY accept to join Germany and Italy in war, to take back Gibraltar. In return, the Spaniards may want French Morocco or at least Tangiers, an economic aid package (to rebuild after the civil war) and of course Gibraltar herself.
OTL, the Spanish took Tangiers in 1940, bloodlessly, on their own initiative (after France was beaten). Neither the British nor the Germans nor the French themselves (who had more important problems on their plate) objected.
That didn't stop Vichy to constantly try to further Collaboration with the Germans (it was mostly them who were reluctant, and only used Vichy when they needed it.
So, if ATL the Spanish enter the war in exchange for Tangiers (or French Morocco), that will displease Vichy French (and make this government look weaker). But if anything, that will also push Vichy to MORE collaboration. In the hopes of getting British territories to compensate for their losses (plus
Belgian Congo). In the hope of getting military victories (hence, pride) on the British (the former ally who sank the Mers-el-Kébir fleet, and alongside the Free French, tried to invade West and Equatorial Africa, and more importantly, repeatedly bombed factories in France proper)
And in the hopes of getting real German concessions (return of prisoners, reduction of occupation zone, reduction of reparations). Better to look like "the government which lost Morocco BUT got back the prisoners, the occupation zone, gained new colonies elsewhere" than just "the governement that lost Morocco". People can forgive the loss of a colony (especially a colony not vital to the country) if things get better at home.
If Wagner is crafty, he can get BOTH Franco and Petain to enter the war together, at the same time. With a treaty that gives France the Belgian Congo (and future colonial conquests) and Spain Morocco.
Then, you can have the Italian, French and Spanish navies, the German, French and Spanish armies, and the Luftwaffe and French air force, attacking Gibraltar together. While French (and then Spanish) troops join the Italians and Germans in Egypt. And French troops open new fronts in Gambia, Sierra Leone, Nigeria, Togo, Cameroun, Sudan.
Next step : take Cyprus and Malta. There, too, Spanish and French navies would be a useful addition.
Moreover, with Spain on board, you can push Portugal to allow the Axis basing rights in the Azores, Cape Verde... Or AT LEAST, be sure that Portugal will NEVER open these bases to British and Americans (like OTL).
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Whether the Nationalists finally won or not, the communist atrocities in Spain (and obvious Soviet support to Spain) will help Wagner cause in the US and British opinion.
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If Spain is socialist/communist, it can be interesting too. For starters, not EVERYTHING would go the German way. Well, almost everything (for 1936-40 at least), but Spain. And I'm sure there can be interesting developments.
=> It would be a near-communist government NOT put in place by the Red Army (even if the Soviets helped), but purely home-grown. And relatively independent from the Soviets because of the distance.
=> Left-wing Spain would likely be more welcoming to refugees from France.
=> ATL, Spanish refugees in France might be Nationalists (that crossed the border illegally), who would happily help the Nazis. Which would be a reversal.
And also some anarchists and trotskyists, who were crushed in Spain by the PSOE / Communist alliance (and would be tracked by Vichy and Nazis too).
=> Wagner will not tolerate (long-term speaking) a Communist country in West Europe, and left-wing Spain will KNOW it. So they will prepare for the inevitable invasion. Which might happen after Barbarossa and British defeat.
=> Left-wing Spain will not dare to enter the conflict except if the Axis looks like it's losing.
=> I'm not sure if Allied Spain would be more a help, a liability or both or neither to the British (don't know enough about Spain military and economy at the time).
=> If Spain goes Allied, there will be a vicious war in the Pyrenees, and it's likely that NEITHER side manages to cross the mountain range for good.
=> ATL Spain might send a legion of volunteers on the Eastern front,
on Soviet side. Maybe send there the far-left hotheads (like anarchists) to get them killed while being useful.
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Oh and, when Barbarossa starts, since Germany already has Norway and Denmark as allies, and will likely have Finland too, maybe try to have Sweden as one further ally ? Swedish help did a lot for Finland during the Winter War, and it was volunteers (even if coming from the regular army), and Danes and Norwegians helped too. If Sweden actually enters the Continuation War, it would put the Soviets under even more pressure.
Not to mention that moving German troops from Norway to Finland (and then the Karelia/Leningrad front) is MUCH easier and faster through Sweden.
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Wagner should secretly contact Rashid Ali. And maybe Palestinian leaders (there was a rebellion that ended just in 1939,
https://en.wikipedia.org/wiki/1936–39_Arab_revolt_in_Palestine ), and tell them to TIME their rebellion.
So that they can start rebelling when the Germans (and Italians and French) are actually in position to help.
Of course, Mussolini was in contact with hardline Zionists (Lehi / Stern group, and Irgoun) since 1937. Those Zionists had a fascist-like ideology and would have possibly listened to a proposal like "put the European Jews in Palestine and create the nation of Israel, ruled by Irgoun / Lehi of course".
If the Axis time things well, they can have a large-scale Arab revolt in Iraq and Palestine (plus a small-scale Irgoun / Lehi rebellion), just when they managed to take Egypt, and just when German (and Italian and French) forces arrived in Syria and Lebanon.
Then, let Egypt, Iraq and Palestine have their independence. The only conditions will be :
=> Opening the Suez Canal to Axis navies
=> Remaining in the war (and maybe provide volunteers brigades, those countries can't provide full armies anyway)
=> Oepning ports, land and airbases to Axis for the duration of the war
=> Providing oil to Axis at a low price for the duration of the war.
Also, let the Arabs deal themselves with the Zionists and do the dirty work there. (Of course, once the war is finished, the Axis can always backstab the Arabs and turn them into full protectorates. After all, Mussolini DID want his New Roman Empire. Basically, have Wagner, Petain and Mussolini pull a new Picot-Sykes on the Arabs).
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Once the Axis has taken Egypt, Transjordania and Iraq, they don't even need to physically conquer the British protectorates on Arabian peninsula (except Aden, to close the Red Sea). U-boats, and Luftwaffe bombings (on Qatar, Trucial States... oil extraction plants and oil rings) would stop the Arabian oil to reach the British. Plus, local population might rebel against the British on its own (and can be supported).
Saudi Arabia was neutral, and will likely remain so (and not provide any oil to British).
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Through Iraq, you also reach Persia, of course. Like OTL, the British will fear that Persia joins the Axis, or that the Abadan refineries (Abadan is VERY close from Iraq) stop producing oil for them. Abadan oil was vital to them.
Then you can have three scenarios :
1 ) British do nothing. Germans pressure Persia to stop producing oil for Britain. Persia doesn't comply, and Abadan refinery continue to work for the British. Then, Germans could invade Persia but it's not in their interest. Too much cost, too long logistical lines.
Then, the U-boats can target the tankers off the Abadan coast, while the Luftwaffe can target the refineries themselves. It's unlikely Persia will declare war over that, with the risk of a full invasion. So, basically, a war limited to Abadan.
British will lack oil.
2 ) British do nothing. Persia stops producing oil for them (on German pressure). Then, either the British still do nothing, or they invade Persia (which is forced into a German alliance). Which leads to next scenario.
3 ) After the Fall of Iraq, the British preemptively invade Persia and try to remove Reza Shah. Then, Persia enters the German alliance. OTL, Persia didn't resist the invasion (which was both Soviet and British). Here, if the British are alone, the Persians resist, and the Germans are next door, the British might be booted out from Central Iran, and then, Khuzestan.
Meaning that the British have lost all Persia and Near East oil, the Germans have lots of ports to carry submarine war in the Indian Ocean, and the Luftwaffe can start bombing strategical targets in India. Not to mention the British can't use Suez and have to take the long way around.
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In this scenario, Wagner could mass armies in Persia, tunder the guise of booting the British from Khuzestan and invading India. While, at the same time, having the Luftwaffe bombing strategical targets in India, and dropping leaflets. And weapons to rebels (like Subas Chandra Bose).
ATL, Britain will look weak at this point. Having lost the BEF in France, then lost Egypt, Near East, Persia. Maybe South-East Asia, if Japan takes advantage. The British will also be forced to deploy even more Indian soldiers everywhere, to raise even more taxes in India...
So, a rebellion could be started. With German agents and Luftwaffe bringing weapons on one hand. And with agent provocateurs riling up the Indian population (for example, shooting a policeman/soldier during a peaceful demonstration, turning it into a bloodbath). Even if there is only a limited and botched rebellion, it helps the German.
Even if there is the FEAR of Indian rebellion (which finally never happens, despite German attempts), it will force the British to leave more garrison in the subcontinent, to less trust Indian soldiers and civilians, and so on.
Plus, the British might come to the table just to not risk India rebelling and joining the Axis (better to have an autonomous / independent India still allied with Britain). Not to mention their oil shortages and multiple defeats.
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Wagner will proclaim that his troops in Persia were here to invade India. But he can use them to start an invasion in Central Asia instead. At the same time as Barbarossa in Europe. Plus, the Luftwaffe will be able to take the war in Central Asia.
If the Germans are good enough, they can say that Stalin started to invade Persia (by faking battles at the border). After all, Russia / SU had always looked south (for Persian oil and ports), and everyone hates the Commies. So, the US opinion might believe Wagner, or at least be in doubt and not clearly see Germany as an aggressor.
And of course, Central Asian people might rebel (like the Ukrainians, Balts... did). Even if they don't at first, Stalin will FEAR their rebellion (he was paranoid). He might start mass deportations, or mass shooting of suspects, or silly things like that, actually driving people to rebel (even if they wouldn't have otherwise).
At the same time, since Axis will be in Syria, Lebanon and Iraq (and Persia), push Turkey to join the Axis. Use the Luftwaffe to bomb Baku. Send the French, Italian and Spanish navies in the Black Sea.
Start landings (through airlifts or sea, through Black Sea or Caspian Sea or both) in Caucasus. And/or Crimea. Encourage rebellion in Caucasus.
Promise Aegean islands, Cyprus, Mosul and bits of Soviet territory to Turkey. About Mosul, don't tell Iraq. The Axis will backstab Iraq later anyway, so it doesn't change anything actually.
About Aegean Islands, Italy can give the Dodecanese. And Greece can be carved now. With Turkey and Bulgaria taking their share, and Italy forcing Greece into a protectorate. It's likely Metaxas won't say "No" if the Germans support the Italians right from the start, and the British are out of the Med. So, Italy gets Greece without fighting.
If Metaxas still says "No", Greece carving can always wait for the end of the war.
In such a scenario, Stalin would be in deep trouble :
=> Attack from west AND south. And if Barbarossa only happens a few months after the Germans arrive in Persia, the Soviets won't have time to build up defences there.
=> Possibly, mass rebellions in Central Asia and Caucasus (on top of Ukraine, Byelorussia and Baltics)
=> Lutwaffe attacks on Baku and any key infrastructure in Caucasus or Central Asia
=> No lend-lease (British or US) through Persia. Nor through Murmansk (thanks Finland and Norway). Maybe not through Vladivostok if Japan joins later.
=> Turkish and Persian troops (even if it's not much) joining the fight.
=> Wagner not treating Soviet civilians as subhumans (maybe planning to backstab them, but later) and actually liberating them (and getting them to work willingly for the German war effort). Maybe THE most important point.
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To sum it up :
1 ) If Spain is nationalist, rope her in. Take Gibraltar. If not, use Spain as a commie scarecrow.
2 ) Rope in Vichy France, too, if possible.
3 ) Have Italians, Spanish and French work together to take Egypt. Send Afrikakorps if you have to (but maybe the three countries together will pull it).
4 ) Better coordination. So, when Vichy enters the war, the Axis troops (and Luftwaffe) are ready to be deployed in Syria and Lebanon. And have the Arab (and maybe Zionist hardliners) rebel at THIS time.
5 ) Give the Arabs actual independence (with Axis bases and access to oil for the duration of the war), and only backstab them (by forcing unequal treaties) later.
6 ) When Iraq falls, depending on Persian and British reaction, either use U-boats and Luftwaffe to interrupt the Abadan production, or help Persia to repel British invasion.
7 ) If a Persian-British war starts, deploy troops in Persia, and boot out the British.
8 ) Pretend to prepare an invasion of India through Persia, while cultivating rebellion (or fear of rebellion) in India. The British might come to the table (or not).
9 ) Attack the USSR in Central Asia and Caucasus, through Persia and Turkey. Whether the British come to the table or not. Having your troops in Persia (with a legitimate reason : invade India) is a GOLDEN opportunity for such a surprise attack. So, even if the British are still in the war, it's worth fighting both at once. The British won't be able to do much to threaten or harm Germany (or Italy or France or any important ally) at this time, and won't be able to help Stalin either. So
it will NOT be a two-front war, merely a two-enemy war.
10 ) Attack the USSR through Finland (if possible, with the Swedish route). If you can, rope in Norway, Sweden and Denmark.
11 ) Cultivate non-Russian rebellions (and Russian rebellions too, for that matter) against Stalin everywhere.
12 ) When Barbarossa starts, use Japan. Either to attack the USSR, to merely mass troops in Manchuria and Inner Mongolia (forcing the Soviets to mass troops too), or to attack Britain (if the British STILL haven't accepted to negociate a peace) south.
13 ) If the Japanese take South-East British Asia, and arrive at the Indian border, there might be a Bengal Famine like OTL (or not). Either way, British will look very weak (and BE weak) in Asia, so, push harder for an Indian rebellion (with support to nationalist rebels, agent provocateurs...). The British will be busy containing Japan (to protect Australia) and holding India, and holding the African fronts (with French and Italians), so they won't bother too much the Axis. And can't touch the Axis in Europe, of course.
14 ) Sooner or later, the Soviet Union will crumble, through Stalin heightening paranoia and violent policies, through loss of territories and resources, through rebellions, mass desertions...
14-bis ) Sooner or later, the British will come to the table. At most, after the Soviet defeat. Until then, they merely have to be contained.
15 ) Once the British and Soviets are down, Japan can focus on China, and win this war.
16 ) While the European Axis members can carve up Yugoslavia and Greece (if it hadn't been done before), and force protectorate onto Egypt, Iraq, Palestine / Transjordania. And Germans can FINALLY start their genocide in the East (for Lebensraum).
17 ) Lots of interestings possibilities, for a multipolar world and alliance systems.