What model of Motobecane? Vitus Tubing?
You might check the tire size of your bike. It quite likely was originally 27". So dropping to 700c, you may be able to mount the tires you desire.
Mounting 650b may be problematic with the brakes.
Isn't part of the sport just getting out and having fun? So, why not?
There are people who modify vintage bikes to take modern components. Or, downtube shifters, bar end shifters, and even stem shifters work very well for shifting gears. No need to extremely fancy.
The one warning I'd say, however, is that French bikes are some of the least compatible bikes with everything else in the world. OK if you're keeping them more or less original, but it could be problematic if you choose to do upgrades of stems, headsets, or bottom brackets.