They did, eventually. Upon invasion the Allies asked General Henri Giraud to take command of French forces in Algeria and order them to surrender. He was unfortunately ignored, but the Allies had already been involved in parallel negotiations with Admiral Darlan to do the same. These succeeded, and French forces who responded to Darlan ended their resistance to the Allies. However, this was rather controversial as Darlan was detested by DeGaulle and others involved in the Free French Forces because of his previous collaboration.

As to why the French resisted at all? It's because those who were loyal to the Vichy regime continued to regard France as a sovereign, if humbled, nation. They therefore believed that what little independence they had would have to be defended against all comers. Of course this is largely overshadowed by the fact that French independence existed at the sufferance of the Germans. A point underscored by Germany's occupation of all of France following the invasion of North Africa.

The Vichy ideal of national resurgence and sovereignty is really super interesting. I would highly recommend Julian Jackson's "France: The Dark Years, 1940-44."