For a long time the US actually recognized Vichy as the legitimate government of France.
A very interesting event took place in our backyard, that few knew about.
The Liberation of Saint Pierre and Miquelon
http://worldatwar.net/article/miquelon/
That wouldn’t surprise me out of FDR.
Many folks also dont know that U-Boats made it into the St. Lawrence River in Canada a good distance and sunk a number of ships.
https://en.wikipedia.org/wiki/Battle_of_the_St._Lawrence
Great point. The United States maintained diplomatic relations with the French government until after it launched an unprovoked attack (sort of like Pearl Harbor) on the French forces in North Africa. Diplomatic relations ended in November, 1942. Admiral William Leahy was the U.S. Ambassador.
Gaston Henry-Haye was the French ambassador to the US during this period. http://content.time.com/time/covers/0,16641,19410310,00.html
Not relevant to this discussion, but some interesting early war material here: http://adst.org/2013/06/the-nazis-take-paris/