The past tense of the verb found is founded, but only when the verb found means “establish" or “begin":
This town was founded in 1730.
My grandfather founded our family business after moving here from Italy.
The other sense of the word found is the past and past participle of the verb find, meaning to “discover” or “locate”:
I found my keys under my jacket.
We found oil while drilling in those fields over there.
So your sentence ("Have you found your keys yet?”) is indeed grammatically correct.
You can find both meanings of found listed in online dictionaries such as this one.