Dia Dhuit!

Like anything Celtic, there is tons of material to sift through on the Internet; some is very informative and some is nonsense! You'll have to be the judge, I guess! I took Celtic Studies and we rarely touched on Brittany. How unfortunate, but that is often the case in many schools.
What I can tell you is that it would be more correct to say Celtic heritage than influence as the Bretons are indeed a Celtic people (Brythonic, to be exact). You could draw an interesting comparison of Scotland and Brittany with regards to language division. Scotland was a nation with Gaelic spoken in the Highlands while Lallans was spoken in the south, close to the English border, a people whose language most resembled theirs. In Brittany, Bretons spoke (and still speak) Breton and Gallo. Breton is a Celtic language closely related to Cornish and Welsh, while Gallo is a Romance language related to French and is spoken in the region of Brittany which borders with the rest of France.