A.S.
It doesn't hurt to call different companies around and check it out. The problem with French Bulldogs: they have lots of breed predispositions. Up to and including skin issues, dental issues, allergy issues. And a lot of insurance companies have exclusions for breed predispositions. Here in Texas we are swamped with allergies and so I have seen several Frenchies with allergy related illnesses (skin/ear infections, eye infections from drainage). Most Frenchies will be over a year old before they start to have any problems so it is wise to get the insurance before they have issues. I have seen it both ways though - I have seen some with several problems and some without.
Some pet insurance have different plans available too so the best thing to do is call around and see what they offer. Be prepared to pay out of pocket up front for any care needed because pet insurance is based on reimbursement. You pay up front to your vet and then send in the claim and they reimburse you.
As far as average vet bills it is going to be largely based on the area you live in. Different parts of the country have vastly different prices so the cost is relative to that area.
I love Frenchies myself and I would love to own one but I too would be looking at the prospect of Pet Insurance if I did.