Fortunately, Frenchies adapt very well to apartment living. They do not need big spaces to roam in order to be happy. We are fortunate to have a large fenced-in back yard, but it is certainly not essential. Frenchies only need a moderate amount of exercise, which can be accomplished by a walk around the neighborhood sometime during the day, a short play time in the back yard, etc.
One caution is that Frenchie puppies should be kept away from dog parks and other areas where sick dogs may have been. Young puppies (less than 12 weeks old) do not have all of their immunities built up yet and could possibly pick up parvo or distemper in grass or other areas where sick animals have been.
Your French Bulldog puppy can also be taught to go potty on a paper pee pad or even on an artificial grass mat which can be placed in a strategic location in the house. This makes it possible for you to periodically leave your Frenchie in the house without supervision for an extended period of time while you are away running errands, fulfilling commitments, etc. We have had good luck in this regard with our Frenchies that we have raised from puppies.