Suncower -> Florimeuh Tournesol
Cowctus -> Cactaure
Chorus Moobloom -> Florimeuh Chorus
Crimson Mooshroom -> Champimeuh Carmin
Warped Mooshroom -> Champimeuh Biscornue
Red Cluckshroom -> Champipoule Rouge
Brown Cluckshroom -> Champipoule Brune
Crimson Cluckshroom -> Champipoule Carmin
Warped Cluckshroom -> Champipoule Biscornue

This is my first time suggesting something on GitHub, so, sorry if this isn't perfect.

While I'm not a big fan of the cluckshroom translations, you can create a pull request!

I never got a notification for this, sobs
I'll try to think of a different translation for cluckshrooms and send a pull request afterwards.
(maybe will just replace it with a chick's sound to match the mooshroom)