Like Retro Grouch says, non drive side is easy. You can actually extract all of the BB parts from the non drive side, clean, and inspect with the drive side cup in place. This will tell you what's worth keeping before you shell out on more tools. The lock ring is seldom hard to remove. You can get a crescent wrench on the flats of the French BB, even with the spindle in there.
Once the parts and the BB shell threads are cleaned up, if the Schwinn parts fit the French bike, and vice versa, then they have the same threads, but by "fit" I mean that the cups can be threaded in all the way by hand without needing any tools or force. This is a case where knowing the "feel" of threaded parts is useful.