I'd imagine a communist France won't be nearly as prosperous(?) as the USSR. The Germans would have annexed most of France's industrial regions after the war and would have control over much of France's heavy industry. Communist France, I'd imagine, would be poor and corrupt for its entire existence, and wouldn't pose a threat to Germany.
The only way a communist France post WWI would be able to compete is if it annexed Belgium, which is not going to happen (Britain is likely still an industrial giant with control over the seas).
Anyway, seeing as northern Algeria (departments of Algiers, Oran and Constantine) are part of metropolitan France, they could come under the jurisdiction of a new government anyway, so Algeria is not a viable option for republican relocation.
I'd like it if someone with more knowledge of France's colonies could help me explore the French Guiana option.
If a Red Paris can't stabilize the economy of what remains of France and then start delivering standards of living comparable to and then exceeding pre-war levels at least for the working classes, it won't last. And of course not just Germany but every power from both sides of the war that has not gone Communist yet will surely gang up on France just as they did after 1789, only much sooner.
The most likely way that a Communist France could survive the first few years would be if all the potential interventionist states were themselves wracked with revolutionary upheaval, or their rulers feared they would be if they invaded France. That seems highly unlikely in the sort of Central Power victory scenario the OP assumes--if Germany is capable of inflicting decisive defeat on France and grabbing its industrial lands, surely Germany is stable enough to put down the Red insurrection, or to backstop a French regime doing it for them, exactly as in 1871 with the Paris Commune versus the new Third Republic.
When I want to imagine a major WWI combatant other than Russia going Communist in the immediate aftermath of the Great War, I picture a defeated Germany going that route. Such a German uprising might stretch Entente occupiers too far and link up with help from Bolshevik Russia; France is too far west to go it alone along that path.
So you'd have to spell out how it is that a far-left regime takes over in France while Germany and Britain look on helplessly or complacently.
But if they did, and were not overthrown by French dissidents in short order, I expect that building on a much higher level of industrialism than Russia (even if the best and most industrialized areas are gone--surely Paris itself was a major industrial area?) they'd start delivering on Bolshevik-style promises of a better life for ordinary people under scientific socialism--then the danger would be Red revolution would tend to spread by example to Britain and even Germany. (Especially Germany, given the extent of Social Democratic loyalties there!) This is why it is ASB to expect either Britain or Germany to tolerate a Communist France even briefly; any explanation of how this nevertheless happens has to explain why the other nations hands remain tied for at least a decade.
Now if such a Red France is somehow established and secures itself anyway, I don't see why anyone outside of France except perhaps the colonized peoples themselves would recognize it as legitimate in the former colonies. The colonists, and the French emigres, would of course hold that they are the true successors of the French Third Republic and not that radical rabble in Paris, and foreign powers would either find it convenient to go along with that fiction (if they want to keep anti-Communist French around) or take the opportunity to take the colonies for themselves, letting the French colonists decide whether to serve their new metropolitan masters or go into exile again. I certainly don't think anyone in Algeria would bow to some commisar from Paris just because he has properly stamped papers!
The only people who might support the new French metropolis's claims just might be the colonized peoples themselves, if the new order offers them a much better deal than the old one was, and does it plausibly, with enough force behind it to hold off other European colonial powers, and it seems obvious to the colonized people that the alternative of complete independence is either impossible or too chancy.
But a Red France, particularly one allied with Russia's Bolsheviks, would probably just denounce all colonialism and unilaterally renounce all their colonial claims in favor of immediate independence of their former colonies. That proclamation would be a dead letter legally of course as the European powers either recognize the exiled French government as the true colonial master of France's colonies, or grab them for themselves. Either way, the Parisian declarations will surely stir up at least some unrest against any and all European masters in France's former colonies and shortly thereafter, all European colonies.
Again the question is, how and why is Red France surviving at all in a non-Red Western Europe. If it survives because it is strong, then the proclamation of liberty to the Algerians is not such a dead letter after all--the Radical Republic's forces will surely descend on any pretender regimes that close to France itself, unless some much stronger European power stops them. But if there were such a power, again--why haven't they already crushed the revolution in France long since? If it is because they can't then the emigres will have to run and set up shop somewhere a lot farther away than Algeria.
The whole thing is I suspect meant to echo the flight of the Kuomintang to Taiwan from China. Well, look at that example--neither regime recognizes the other's claim to anything; both regard each other as outlaws and usurpers. But the PRC does not invade Taiwan mainly because it would risk global war doing so--and Taiwan of course doesn't invade Mainland China for the same reason that salamanders rarely try to eat tigers.

Taiwan shelters under the protection (often, for political reasons, veiled and indirect) of the United States, just as an emigre French Republic in Algeria might be protected by the Royal Navy. But they certainly won't obey any orders from Paris any more than Chiang Kaishek listened to Mao. Nor will their European protectors listen to Paris on the subject of the former colonies, even if they do evolve a detente on other subjects.