Not sure if the distinction between accent and pronunciation is very relevant here? I have a particular/personal 'French' accent that heavily influences the way I pronounce words. As stated, it mainly comes from the way I learnt : I often straight up applied french pronunciation (but with some basic informed knowledge of what could be the proper way) to what I read. So, to answer your examples, I pronounce those exactly like the french "beau", "tire" and "rot".

For me, English has been a mostly literary language for years with most spoken forms coming to me with simultaneous subtiles. So, it's rare that I encounter a new spoken word that I haven't read before, but with time and familiarity you develop some kind of heuristics I guess (and enough of English comes from French that there is no need to be too lucky).

I now live in Japan and used to guide, in English, foreign tourists in Kyoto. Amusingly only native speakers seemed to sometimes have difficulties to understand my strange pronunciation/accent.