My french bulldog is almost 4 months old. And we have had him for almost a month. He has not stopped throwing up since we got him, it is usually clear or foamy and sometimes has just a few pieces of kibble in it, we have took him to the vet countless of times and they say he is clear , but I just can't believe that. Because they haven't checked for everything. But it usually only happens when he gets excited or drinks quit a bit. But we lowered how much we give him in water. We only give him about an 1/8 of a cup of water every hour or so. It seems to help a little but he is still vomiting frequently.
Any answer I would greatly appreciate.

Honestly there are a lot of things that can cause vomiting after eating and it would be impossible to give you a difinitive answer online.

I'm not a fan of posting links but this site has great detail into the causes of vomiting and offers some suggestions as the what the problem may be:

Causes of Vomiting - Why Your Dog is Vomiting (http://www.dog-first-aid-101.com/causes-of-vomiting.html)

I will add though, has he been on the same food the whole time? It could be a dietary problem. It could also be a problem with the throat, have you tried feeding him from an elevated bowl before?

Have the tested for regurgitation problems? The most common reason for regurgitation is an obstruction, but I would assume they did x-rays and such? When he vomits is it forceful with a lot of retching and drooling and is it accompanied by yellow bile and sour smelling? Or is it mostly undigested food in large solid like clumps?