Unfortunately, France is consistently where I have had the worst experiences in restaurants regarding food allergies. They just don't 'get it'.
First of all, there is generally no willingness to alter food prep to accommodate allergies. Often, the patience to discuss how exactly food is prepared (ie use of butter) is totally absent. Nor is there always the sense of responsibility that comes with answering truthfully or completely. Nor can you assume that if you ask about the presence of milk or butter or cream, AND state an allergy to milk, that there will not be cheese in the food (since you forgot to specifically ask about cheese as well - no kidding.).
Your daughter's friend will have to accept that he/she will a) be taking risks, b) be very limited in food choices, c) always have 'fall-back' food with her in a pinch.
She will have to ALWAYS say "aucune sauce, s'il-vous-plaît". Be prepared for pugilistic attitudes when they get it wrong or don't understand.
She can't be shy. She will have to be prepared to send food back to the kitchen (and refuse to eat what comes back - I have had veal come back 'scrapped off', even though I had been clear about 'no sauce' when I initially ordered).
Another time, I had to refuse fresh fruit because it came with 'crème anglaise', even though I had declared the allergy and specified no milk or cream when ordering the meal. According to the waiter, I had not asked specifically about 'crème anglaise' - thus MY bad. One of the things he said was that people say that they have allergies, when in fact it's 'a caprice' (being finicky).
One night, I actually could not eat anything at all and left dinner on an empty stomach. We were a party of four and the problem(s) arose when we were served - too late by then for us to go elsewhere.
I have been to France multiple times and have criss-crossed the areas that you intend to go to. Regarding the response to allergies, the best food experiences were in Paris, and the worst in the provinces. I speak fluent French (raised in Québec), so the problem is not language. It's one of personal attitude and culture. I say 'culture', because the Italian approach to accommodating food allergies is much more open and willing (in marked contrast to the French), for example.
I know that some people here will take exception to what I just wrote, but it's what actually happens. On this subject, I'm brutally harsh. Just be prepared that it won't be easy and that a few idiot waiters/owners will be more than willing to put her at risk, because they really won't care to understand/take the time/accommodate.