I think it's unrealistic to think you could raise a child to be bilingual in this way. Exposure to the language and some vocabulary, yes but I think bilingualism would generally need a native speaker parent or community language.

My mother tongue is English, I live in Germany and have spoken English to my kids from birth, I wouldn't say they are bilingual even, more fluent in English. I do find it hard some days to stick with it though especially as there many situations now I don't have experience of in English (school stuff for example) so it's easier to say it in German. But at the end of the day foreign language exposure is good thing, so maybe find some children's programmes she can watch and pick a day when you only speak French to her or something?

There is no harm in including your daughter in your language acquisition, but bilingualism will be hard to achieve. DH's first language isnt English (tho his strongest language now is English, because it is his language of school and TV and socialising) and he has struggled to get the kids to keep their second language on par with English.

To be blunt OP, I think it's unachievable for you as a mum, and also will be very hard work. I have bilingual children raised via the OPOL method and that was (is) hard enough. I'm fluent in their other language, but don't have the childhood cultural references in that country (nursery rhymes, songs, fairy tales etc) which are so important for young children's language acquisition.

If you're good at languages and she sees and hears you learning them, she will naturally be interested, will probably want to copy you, and will probably be very good at them herself.

If you really want her to be fully bilingual, consider a French play group and/or weekly language lessons with a native speaker. I know a very dedicated mum who did this from when her son was 3 until he was 18, and he ended up completely bilingual with no accent, despite never having lived in the second-language country. It was really quite impressive,and gave him a huge advantage jobwise. Bonne chance !

My mum was pretty good at French and used to put French tv/tapes on for me and when I was learning words, she would put stickers in French and English. Then when I was old enough, I went to French classes. I think it is much easier nowadays to do this but I think you should learn it at the same level.

Where do you live? It's not an unachievable goal, but you can't do it on your own. There are some fabulous French schools in London (Ealing, Clapham, Fulham to name but three) - starting aged 2.5 in maternelle - with falling rolls due to Brexit. Fees are reasonable (nothing like an English private school). If you enrolled her in one of those she would become bilingual - and would have lots of French speaking friends. You can't do it on your own especially if you are not fluent yourself (even children with one French parent can struggle to become bilingual if they grow up in the UK - I know several).

Good luck. I’m a native speaker and my DDs refuse to be bilingual. It takes a lot more dedication than I had.

I’m bilingual too and found that raising children bilingual is a lot of work and effort.
If your aim isn’t for your dc to be bilingual as such, then the one they should learn is sound/accent which you won’t be able to do. I mean I’m french, dcs raised bilingual and said dcs STILL don’t have a fully french accent. It’s not french spoken with an English accent but it’s not a french accent either iyswim.

I don’t want to discourage you. But I think you are being naive there

This is why mothers used to hire French or German governesses.