If France really fights on do Richelieu and Jean Bart head for the Clyde as original planned?
Does Richelieu still suffer gun explosion?
What becomes of Jean Bart, spares for Richelieu, completed as carrier or completed as battleship in UK or USA?
At the very least, I do see them being evacuated.
Timeline changes don't fix mechanical problems, so likely yes.
Spares would be a bit of a waste, and between inch conversion necessities, and overcrowding of British and American shipyards regarding BBs, the second isn't happening in my opinion, so likely a CV.
Second would be whatever Italian naval interdiction there eight be with the Traffic between the souther port group & Africa. What happens there depends on how aggressive the Italian get. A secondary factor is Brit assistance from the fleet based at Gibraltar (I abased in the Tunisian ports m not sure if it was labeled "Force H" in June 1940.) I don't think they were hunting surface raiders that summer, so they ought to be free to lend a hand. Based on the track record OTL the Italian submarines are likely to be the most successful here, tho with the density of French warships in the traffic submarine losses would be at least at their historical levels if not higher.
Aggressivity wasn't exactly the Regia Marina's strong point. Besides, when you see how ill-prepared both the ground and air forces were, I doubt that much ships could be sent for raiding. And yes, the Force H is probably kept around without corsairs and such an operation happening. I'm also doubtful about Italians' submarines. Not just because of te initial availabilities, but also because of the volume of escorters available, and the fact their standard tactics are 'one zone, one sub'. Coordinating a mass attack with that seems... problematic. Ships will be sunk, but not tht many, and losses are to be expected.
At some loin the Italians are going to try to attack Corsica. That may be tied to interdiction of the evacuation, or come later. How this Leone Marino might develop I'll leave for later.
Sorry, not really seeing that one as possible. They didn't try for Malta OTL, why risk it against a biggest target with more opposition when means aren't any bit better? In summer, there will be no fighter to cover anything: units with G.50 are busy on Metropole for all of July, CR.42 aren't exactly that available both because of the Alps offensive and the Lybian hemorragy, and MC.200 aren't back inunits before September, and there is the time to effectively distribute them, and train the pilots to the new mount where most of them had biplanes in the past. Without talking about the CR.32... And it will be Cr. 32, Ufficio Storico's records give a number of 50 fighters/month in 1940, 20 of them CR.42, and 15 MC.200. Reequipping will be a painful slog.
Also, no torpedo bombers in meaningful numbers, so burden of the battle to secure the shipping lines necessary fall on the Regia Marina alone, which is already lacking BBs, and is still badly outnumbered, and such a move would trigger a massive Allied answer for the threat to evacuation it would cause.
Besides, with what ground units? Italians had to wait 11 days after war declaration before they managed to get the supplies for an offensive OTL, I'm not seeing this as a good sign of how fast and how much forces they can muster for this invasion. Especially since the French will certainly be reinforcing the island on the ground and air front to keep it. And later than summer is too late: Allied fleets are free from the evacuation's burden, and this timeline's version of the Taranto raid probably happened, leaving the Regia Marina unable to win that fight without German air and para support.
The fourth might be called the Sicillian Straits battle. From July the Italians start mining the strait. At least the French destroyer group based in the Tunisian ports would be interested in this. While part would be operating further north covering the evacuation its in the Allies best interest to keep the strait open, so its likely there going to be a series of engagements developing with French and Italian light forces, initially at night. If the Italians break off the effort thats as far as it goes. But, it could escalate with both sides adding cruisers. If escalated this battle will overlap the end of the evacuation battle, and carry on after.
There would be a air battle over the strait as the air forces of both side attempt to intervene, and a separate effort to raid each others airfields in Tunisia and Sicilly.
Next would be simiiar to the OTL battle that developed in the central & eastern Med. Each side sparing as they attempt to reenforce Malta and Lybia.
I'm sorry but again, I'm ot seeing thsi happening. Facing heavier naval and air opposition ( French Aeronavale can reallocate units with training to attack on Malta ITTL for instance) will incite the Italians to even more prudence than OTL. Minie fields will certainly be done, and fleet movements to secure the Mediterranean, but the Italians will probably avoid bigger battles unless they really can't, because they're the outnumbered ones, and the replacements in naval units they can manage are inferior even to the British alone. They can't waste ships, especially when each new ship lost makes the risk of landing invasions in Italy bigger. And I'm thinking about another point: More heavily contested Mediterranean Sea can lead to the Italians reallocating a non-negligeable amount of resources for coastal fortifications, and their war industry...
Nah, I think the Italians will avoid battles in a strategically defavorable situation, leading to this timeline's Taranto raid to seek them in their harbors.
Should the French gain a few days from OTL they just might march 8. Army out of Alsace into the Rhône Valley; when Guderians Panzers arrived at Besancon on 16. June French engineers were preparing the four bridges for demolition. The Germans reach Dijon the following day and then move up the Swiss border to close the trap on the French Army Group in Alsace-Moselle.
I'd say that's why FTL placed the divergence in military operations on the French side at 10th June (Weygand replaced with someone accepting the idea of leading a general retreat/evacuation): so there is still time to get the men in the east of the country before the Germans can trap them all.