Everyone knows that the French, in the 19th and 18th centuries, colonized many parts of the world, including Quebec, Louisiana, Algeria, the Caribbean, a tiny spot in South America, a large chunk of Africa, and Indochina. What are some areas in the world that the French could have colonized as well, because of their own interests, or just places that would have made sense for the French to colonize? Although, my question excludes India and Australia- the French did colonize India, but the British were too strong there, and they wanted to colonize Australia, but unfortunate circumstances led to it not happening. Besides these 2 areas, what were some other places the French would have most likely colonized? Thanks!
You forgot a few islands - Madagascar, Réunion, Maurice, Nouvelle-Calédonie, and a sizeable part of Polynesia. If XVIII century wars go better, they can keep a bit more of the first colonial empire (Newfoundland, Saint Kitts...).
For your answer, it depends on your time-frame. To keep it short: XVI century in America, XVII and XVIII in Asia, and XIX in Africa.
I think the big one is Brazil. France tried tried “France Antarctique”, in the Rio de Janeiro bay, and “France équinoxiale”, around the equator. Making any of these successful is not a very heavy POD (after all, Guyane is still French). In the Americas, there is also the failed settlement in Florida. And the Falklands Islands are known in Spanish (and French) after the city of Saint-Malo, which hints that they could also go to France.
Another rich possibility is Asia. Thailand was another near-miss in the XVIIth century, and either Hainan or Taiwan seems possible as well. Maybe some island in the Philippines or New Guinea could be of interest (although Philippines = confrontation with the Spanish, which is bad; and New Guinea is notoriously hard to settle).
Apart from this, in Oceania and Africa, the French were all over the place enough that I don't think it very likely they could have invaded much more. (A possible exception, in the XIXth century, would be completion of the French Sudan project, linking Djibouti with Sénégal; or maybe Egypt if they can manage it
before they dig the Suez canal).