I've been researching this issue for months!
My boy is very small as well. He is currently 6 months old and only 11lbs.
I've looked at a few weight predictors and they are predicting 13-16lbs for his adult weight.
Looking for a Puppy Weight Chart? (<If you want to check it out)
There was a thread on here I found awhile ago where someone had put together a chart of a lot of peoples french bulldogs weight stats & ages.
A lot of the weight gain times varied pretty drastically. some gained the bulk of their weight between 6-12 months and some gained the bulk after they hit 1 year.
Some that were "runts" or fairly small ended up being 30+ lbs and some of the bigger puppies plateaued and stayed under 20lbs.
Its crazy how drastically different each french bulldog is, it makes it so hard to predict their approximate size.
(I know this doesn't really give you and solid info, I was hoping my thoughts might help)