I wondered if the Wood elves have their own language? I think not but I do wonder. Thank you.

I think they do, but they prefer to speak the basic language of Tamriel when away from home. I'm sure if they ever make a game in Valenwood we will see them use some of it. Like the Dunmer did in Morrowind with Sera, Muthsera, and N'wah.

I would love that.

The speculative language origin chart on UESP says one may be derived from Aldmeris.

http://en.uesp.net/wiki/Lore:Ehlnofex_Languages

Of course, as stated above, UESP notes that it is entirely speculative. As far as I know, there is no actual information on a Bosmeri language, but my guess is that one exists although there is a good chance it is not in general use (perhaps because they are part of the Aldmeri Dominion, they primarily speak Altmeris/Aldmeris). I would also venture to say that each playable race has their own language used to some extent in their native province, and some we definitively know do.

If the Bosmer don't have a unique language, then maby the Centaurs of Valenwood will.

They do, yes. We could learn their language, Centaurian, in Daggerfall.

Based on the naming of wood elves in the TES games it seems they speak Sindarin

As in lotr?

oui