Quote from SummitAP
It is an SI unit that came from metric, but the metric prefix system, including centi- prefix, is LATIN not French. (Yes, French is a romance language, but we don't say other French derived words that way). We do not pronounce direct-Latin derivations with French pronunciation, particularly if the word has been present in English for centuries.
Yes it comes from the Latin (centum=hundred), but it is also true France is the origin of the metric system and modern science (or at least modern chemistry) spread from there. Therefore, it is reasonable that in some regions, French pronunciation is used as the norm.
Having used metric system in my native country where all that is western came from America, I've always said and heard sentimeter. A friend who came from Russia tells me that it's pronounced sahn-ti-metre in Russian.
I say no big deal. Both are correct. I'll go with the majority though. In my experience (in US) I've only heard the sohn- pronunciation from two of my nursing professors, and senti- pronunciation from countless other professors of nursing, chemistry, physics, and mathematics.