ComradeOm said:
Which is akin to suggesting that in a similar scenario the US could have fought on from Hawaii. Your case seems to be that the French military should have either extensively prepared for its defeat prior to the war (and thus provided a major logistical and operations base in Algeria) or, in the space of a month, somehow exported its entire military and logistical infrastructure and assets in order to put them in the hands of the US and the UK
Many of the flaws of your comparison have already been covered, but a really glaring issue is the French colonies in total
had a population twice the size of France proper. Remember it isn't just Algeria were are talking about here since the French colonies included much of Western Africa, as well as French-Indochina along with a variety of other smaller possessions. While there were limits on the support they could count on from the non-ethnic Frenchmen, they still could get plenty of support overall. The situation simply didn't even remotely resemble your example.
While there are limits on how much could be transferred over in time, France could definitely still transfer over plenty of equipment, and many of the aircraft had ALREADY been transferred over by the time France surrendered historically. They won't be able to transfered everything logistically, but they can cover many of the key elements.
As far as the navy is concerned, its very easy to move active units from bases in France proper to North African ones. France also had some substantial naval ports in North Africa which they would be able to utilize. It also is true that they would probably CHOOSE to deploy some of the units to help the UK while basing them in Great Britain.
An obvious mistake you're making is that with those colonies its definitely not a matter of simply putting its forces into the hands of the UK and the US. Its true that in the long run France will need significant supplies from the US or the UK to keep its units functioning effectively, but France always has the potential threat of of seeking a separate peace with Germany to leverage against the other allies in this scenario. If anything the French position might actually be stronger if they eventually negotiate with Germany in this situation given the remaining French forces are in positions where its hard for German forces to to try to reach and attack them. Basically if the allies try to compromise the French forces too much, the obvious French alternatives should ensure that France maintains its own bargaining position and doesn't end up with it being forced to simply use its forces the way the allies want them to.