Modern English far prefers cliché, with the acute accent, to cliche. The noun comes to our language from the French technical term for a stereotype block—a metal mould plate used for mass printing. Both cliché and stereotype developed their figurative senses by the late 1800s, at first meaning roughly the same until diverging into their modern definitions in the early 1900s.
When treated as an adjective, both cliché and clichéd may be used, though the latter tends to sound more natural to English speakers, as it matches other English adjectives formed from the past participle of verbs. In French, cliché already is the past participle of clicher (to click), so clichéd could be considered a double past participle—in French. But since we’re speaking English, it is not only accepted but also preferred.