Did the lore really meant for her to be French though?Yeah, from the lore, it seems that way, but she is definitely American. She uses the imperial system, anyway.
There was the "flag of the freedom" part but it could easily mean the US flag as well instead of French. In fact I actually thought of US flag before someone brought up that the French flag also represents freedom. Another point I have seen being brought up was "Gigi" being a French name, I try to search for the name in Wiki, and there are more Americans named Gigi than French.