Would/could you use this to say František is sad/depressed or simply that he is now the color grey?
Just the color grey. This phrase has no connection to sadness or depression
What does this mean? Why would anyone say this? Did a bucket of paint fall on him?
I am not sure myself. Sounds like he was a victim of an unfortunate event involving a can of gray paint. If we meant to say that he now has gray hair, Czech would say František je teď šedovlasý. Or František má teď šedé vlasy.
As it is it sounds like we Photoshopped Frantisek and robbed him of all colors.
There is one more option. Frantisek is playing Sorry! "Člověče, nezlob se!" and somehow got gray pieces to play with. We often say "i am red, blue, green..." when playing games involving colored cards or pieces instead of saying more logical "I have red, green, blue pieces".