Right ok, well this is from a uni module i took. Prepare for a total info overload!!! Bare in mind its taught from a british view aswell. I will try to explain them well but breifly u might wanna google stuff if u want a better picture?
Well, like i say theres no yes or no, it more so depends on what you beleive on how language is acquired. Theres the Chomsky theory of the language acqusition device, this is a kind of natural view, that beleives that language is a biological makeup of our brains. Then theres the empiricist view which says language is learnt from experince (which is what could be more so argued for what happens in bilingual homes). Its probably advisable that between french and english you choose one language as your main language and then introduce the second language at a later stage (how late i couldn't tell you if i'm honest). The empiricist view states that first languages are beleived to be picked up through a trail and error hypothesis formation which is why children begin to say things like 'i dided that' (correct version being i did that) the -ed comes from the rule they learnt for the past tense -ed. So when you introduce a second language at a very early stage it can cause confusion because of the different rules that need to be learnt from each. Empiricists and nativists also argue whether a second language can be learnt competently. One leaning for and one against. IMO though i do think it probably depends on the competance of the child and the people speaking around it. My friend for example is fluent in two languages as her parents 1st languageas are different and although i don't know her second language seh seems to speak it with confidence and is understood. Like i say probs best look them up and make your own decision, just try not to get lost theres allsorts of theories that are linked! As for ASL, we're talkin about american sign language yes?, thats fab to get your baby to learn it but again you need to becareful they don't get confused. Some hearing children can sign before speech and vice versa, deaf children can babble. On a basic level, for a hearing child Its to do with the phonemes (sounds) that are picked up when the baby hears your voice, thats how people such as chomsky again beleive they learn through whats known as the critical period hypothesis.
Right i think thats info overload. I've tried really hard to keep it simple (and hopefully not made it worse) but its so complex! I'm totally on the fence personally, i really don't know whats best. I don't know if you can get them over there but here they make infants leapfrog toys aswell that speak different languages
https://www.leapfroguk.com/do/findproduct?id=bilearntable_uken&ageGroupKey=ages_infant
https://www.leapfroguk.com/do/findproduct?id=bilearndrum_uken&ageGroupKey=ages_infant
etc. Just ask if u don't understand anything
but I'm sure babies would be able to pick them all up just fine. It amazes me when children are bilingual from an early age- it's fantastic. I wish I could. I learnt French at school, but I'm far from fluent in it. I'd go for it, you'll have one intelligent lil girl on your hands by the time she can speak! 
