I teach EBM in French and there is actually not a good translation of that term that will satisfy linguist and users of EBM

Strictly speaking EBM should translate into "Médecine factuelle" (factual medecine) but this doesn't mean anything to most people. Many use the term "Médecine basée sur des données probantes" (medecine based on convincing data) which doesn't flow well in conversation but seems to represent the concept better. Frankly, in spoken French (at least in my part of Quebec), very often people use the three letters (EBM pronounced in English) as a term in itself because they feel it grasps the concept better. So the term "EBM" would be embedded in French phrases.

It was interesting to see that in other language the word evidence (spells the same way in French) doesn't mean what it means in English. In French too it has the meaning of evident.

I recently had to write a letter about EBM to different people and I used the real French language accepted term of " medecine factuelle". I had to put the other term in parenthesis just beside it because people would not grasp what the letter was about without an explanation....

I will have to write for a French medical periodical about EBM in about a year and I know they will want me to use "médecine factuelle". I hope by that time the expression is more widely known so people know I'm talking about EBM....

Final comment

In Quebec a judge would use proofs not evidences