Apparently, the equivalent of "physicien" in Old French, "fisicïen", meant "physician; medical doctor". How did it shift its meaning from "physician" to "physicist" in modern French?
The answer lies possibly in the construction of suffixes for occupations: -iste and -ien.
While in English word-building the name physic-ist is accepted, in French it would not sound quite right.
For example "violoniste" sounds right, but "violonien" would not sound quite right because it contains a repetition of the same sound io/ien (presumably because it more effort to pronounce right). Similarly "physiciste" would contain a disgraceful repetition of the sound si/ci.
Physics (at least the name) has been in vogue more recently (before it was called "philosophie naturelle"). Since there was only one slot available for physicist and physician in French and since the word "médecin" was already in wide use, the physician gracefully left his place for the physicist.
Indeed there is no "medicist" or "medician" in English; in the end, it was just a matter of which words would sound appropriate according to cultural preferences.