Nice mopeds you've got there. You'll love them. I've been living with a 1977, 1978, and 1979, Motobecane for a number of years now.
I've had something similar happen before. Once they got flooded, they wouldn't start until I did this: pull the plug, let the engine evaporate the gas from inside the cylinder, and put in a brand new spark plug. Then try starting it up. Also, if their new to you, I'd clean the carb really well.
Also, as Stephen said "Sounds like you definitely need to close the petcock of both bikes every time you shut down." This is great advice. I found myself needing to do this as well.