Yes, they are, and have been since NATO was founded. From 1966-2009 they did not participated in the Integrated Military Command Structure, despite remaining fully in the alliance.
They still don't participate in the Nuclear Planning Council, and their troops are not put under permanent UN command in peacetime.
France is part of NATO. They backed out of the integrated command structure in the 60's (but still remained an treaty member) and rejoined in 2009. I think they still reserve the right to not put their nuclear arsenal under allied command.
Yeah I see now France is back. I know they were a founding member of NATO I'm not doubting that. But they left in the 1960s...sort of, but were in sort of but separate, then back in for sure in 2009.
France may not like that. They're not in NATO. But they have nuclear weapons.