Should they be mobile? how would they communicate? How would they react to harvesting their fruit?
I never so much as considered this sort of thing in any of my games, even though Ents, the Aldryami, and the various plant peoples in Stapledon's Star Maker were part of the genre background. (My exposure to the possible motile sentient plants of SimEarth came only shortly before my burnout.) But I do have one war story about them.
It was one of our “armageddon” games — a bring a couple of characters for a wild weekend's gaming — back in the mid 80s, aimed at superheroes and using Champions. As some players were lacking any Champions characters, they brought along character concepts for statting up. One of them was Pete Windsor's character, Falain, a sentient, motile tumbleweed, with a Judge Dredd-style hoverbike — apart from that it was generally a Pete character (aligned chaotic-daft); apart from its making disparaging comments about animals (the other PCs), I can't recall any other details at this decade-plus remove. ISTR that was also the game where another player had a swarm of killer bees — People's Attack Regiment #5 — with a yellow rain area effect NND.
Not quite a sentient plant war story — One player's non-gaming wife,
had managed to take on board, from games being held at their house, that
Gloranthan elves were walking sentient plants; so some while after the
Glorantha game crashed, and we were playing Shadowrun, she
commented, à propos of something that the elf street samurai did “But
aren't you supposed to be a lettuce?”
The character was ever after known as the Electric Lettuce.