The reason why your dd doesn't want you to read to her in English is because you have a relationship in French. Speaking English with her is very unnatural and uncomfortable for her. It's not the English she's objecting to but the fact that it's you using it.
I get the same darned thing in my house. I lived and worked in France before meeting my non-English speaking French husband. My kids hear me using French all and every day. But try to say ONE word to them in it and they get completely unglued. They are a lot older than your dd but even in their French world, they associate me with English and that's what they want me to use.
We put them in a French-German bilingual program when they were about the same age. They picked up German in a heartbeat. All three are top students in their classes and the older two are trilingual. I can't claim (yet) for the youngest but she knows a lot of words.
I've also seen many non-French speaking children go right into French school at age 3 and pick up the language within months. We have a lot of refugee families who don't speak French themselves but the children are fluent. I can't count all the awkward times I've greeted fellow parents in French just to get that blank look, or a meek "bonjour" while our children are babbling away to each other. I thought one dad was just stand-offish, only to take the time to speak with him and his very hesitant French... His daughters speak to each other in French at home.
Whatever you do, do NOT try to "teach" her any English ahead of time for a number of reasons. This doesn't serve any purpose and she might get rebellious towards the English. Instead, talk to her about learning English. One friend would go out in public and say to her dd "Listen to them speaking French. You're going to learn to talk like this when you start school..." Answer any questions she has about it. She can watch T.V. or films in it but don't interject anything.
What I can suggest is that you tell the teacher that she doesn't speak English. This is important to know if there is anything serious. Also, the teacher might just want to confirm that your dd is following along and knows the instructions. The little girl above became an excellent student and only had one bad incident, when she didn't know that they were using a different classroom one day. They found her in the old one.
We also had an incident where another parent (from another class) yelled at my child in front of the whole class. My dd was so upset she couldn't express herself in either English or German. The teacher immediately switched to French (notice that she would only talk to the teacher, not me, in French). Yes, it was a whole hooplah with the director involved and the mom called in... but the point is that if there is something dangerous or immediate, they need to know.
Actually, I've seen all-one-language programs work better at this age often than bilingual programs. Sometimes children who already speak both find that the level is not suitable in one or both languages. One friend's child became the "English" child and was bored stiff on English days, while not following on French ones. In an all-one-language program, children this young don't know or care who speaks what. They follow the others and just absorb it as they go along.
The most important factor is that the school is good and the right atmosphere for your child. You want to be zen about the teaching philosophy and the program they're teaching. Language is important but don't place it at the top of the list. If there are problems, don't immediately blame the language (happened once with one of mine) but look into other factors. My son needed better study habits but the teacher was too quick to blame the German and English on his problems (sorted out with some intervention and now he's on a roll!)