You've tried shouting at him and swatting at him, but this only seems to get him more excited and he keeps coming back for more. Much as you love him this is beginning to feel like an uphill struggle, especially since the kids are now getting screechy whenever for the puppy is near, in anticipation of being bitten.
You don't want to give up on him, but equally, you can't risk him biting the children.
What to do?
However, puppies also have needle-sharp teeth and if they decide your hand is a great toy, then this can be very painful for you.
Teaching a Frenchie pup not to bite is crucial, since what starts with play in a pup could become a serious problem in an adult dog. Training plugs into the principle of bite inhibition, which is where the pup learns to moderate what he does with his mouth and avoid contact with human skin. This is done by reacting in a similar way that his littermates would if the pup plays too rough a game.
In addition it is helpful to have: