Assuming it is even POSSIBLE to convert your Motobecane (and it hasn't been established that it is) it would probably cost ten times more to do than your entire bike is worth.
What's the big advantage of having everything run on the same fuel? Are you planning to go on a campaign somewhere and will have a fuel truck in tow? Are you going to convert your outdoor grille, kitchen stove and water heater to diesel while you're at it?
Better yet, maybe you could convert your moped to atomic power. Then one little chunk of Uranium-235 could keep the sucker running for the next 100 years without refueling! That probably wouldn't be much more difficult than converting to diesel. And would make about as much sense.
If you really don't like your gasoline-powered moped, I'm sure you can find someone to take it off your hands for you.