However, it is not legal to pick any flower — including the California poppy — or any other type of shrub or tree or growing thingy if it’s anywhere on state-owned land.
The many letters of the law
California Penal Code § 384a explains it all in a very succinct 794 words, but the bottom line is that if it is “growing upon public land or upon land not [your] own” — such as in a park, at a school, on a median, or even outside the county courthouse — don’t pick or otherwise hurt it.
Harming that plant life could be considered a misdemeanor offense, and get you a fine of up to $1000 and as many as six months in county lockup.
(Depending on what you’re into, it might be important for you to note that this rule applies equally to “leaf mold on the surface of public land.”)