Perhaps it is worth making a list of pros and cons :
Pro
More exposure to French than at the moment, makes French more than "dad's language"
At the end of the street
Languages not mixed in the same environment, always and English or always French
Con
Child happy where they are
Child will assume only be there a short time before starting school
Could be Pros or Cons
more / less expensive
bilingual nursery leads onto bilingual school yes / no
I do know there are several mums and tots groups in London for native speaking French children, if you are not already attending one, worth trying out, hopefully you will be welcomed as the speaker of the other language, doesn't always have to be the French speaking parent attending hopefully.
Wouldn't worry in the slightest about the poor Chinese, certainly not at 3 years old, 3 languages takes typically a bit longer to learn than 2 or 1, Chinese is always likely to stay weaker than English if you live in England. I'm sure there is a network of Chinese saturday and sunday schools for when your child is older, which you probably already know more about than anyone else reading this.
One last thought, since your child is already being brought up in a bilingual environment, let's hope the nursery would not see you as a "good catch" to help out a class full of monolingual English speakers whose parents wish their loved ones to pick up French, make sure you ask what the linguistic backgrounds of the other children likely to attend. I'm only adding this comment after hearing of comments from mums who have removed their loved ones from French / English envirnoments near me where their child have learned little English or French due to the class being full of German / Finnish / Swedish speakers - other languages are great but it's a fine line balancing the proportions in a class, when there is a large proportion of children speaking another language between themselves, it is hard to persuade the children to speak the target language. Our children's school has 30 nationalities in it and they spread the children out so there are never too many anglophones or hispanophones together for example to the detriment of the French target language.