In this context, “environ” would be an incorrect translation. It only means “about” in the sense of “approximately”, “more or less”, or “thereabouts”.
For the sense of about that’s about “relating to”, which you’re using in this sentence, a better translation would be “à propos de” :
I would like to tell you something about my sister.
Je voudrais vous raconter quelque chose à propos de ma soeur.
As is often the case, there’s no 1 to 1 translation of about in French.
Environ only translates as about when it marks an approximate quantity:
She was about ten = Elle avait dix ans environ // Elle avait environ dix ans
When about is an adverb, it translates as an adverb or an adverbial phrase in French too:
I was about to leave = J’étais sur le point de partir
When about is a preposition marking the topic of a conversation, a speech, a book, or the like, there are three main options:
de: It only has this meaning with a few verbs, but this includes a very important one: parler (also discuter and causer, all essentially meaning speak about). Your sentence could thus translate to:
Je voudrais vous parler de ma sœur – I’d like to speak to you about my sister
sur: This is the general preposition that’s used with most other verbs (and it can be used with parler too, although with a different meaning in some dialects)
J’aurais aimé vous dire quelque mots sur ma sœur – I’d have liked to tell you a few words about my sister
à propos (de): unlike the other two (the most and fifth most used prepositions in French), it’s unambiguous and can only mean about. It’s however quite a bit clunkier, clocking in at four syllables and is mostly thus used for maximum clarity or in verb-less sentence fragments:
J’aurais aimé vous dire quelque mots à propos de ma sœur
Even then it has a meaning that’s not shared by English’s about:
À propos de ta sœur, elle se l’est enfin payée, sa liseuse Kindle ? – Speaking of your sister, did she finally buy herself a Kindle?
À propos can also mean by the way.
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