With regard to spelling, "cliché" is a word borrowed from French. In French, "cliché," with an acute accent, is the correct spelling. In English, the commonest spelling is "cliché," but "cliche" is listed by dictionaries as an alternative.
In other words, "cliche" is fine.
It is not written with a circumflex over the (ê).
Often, a word borrowed into English will retain its original spelling and pronunciation for as long as people still think of it as a foreign word. Over time, diacritical marks will be lost, spelling may be Anglicized, and pronunciation almost always is.
For example, Jack London wrote a story which, when originally published, was entitled "All Gold Cañon." That is, in 1906, people still thought of "cañon" as a Spanish word. Now, it is always written as "canyon."
In the 1950s, the word "role" (as in a play or movie), was often spelled "rôle."
I've seen the same word--meaning "summary of work experience"--spelled as "résumé," "resumé," and "resume." The only possibility I haven't seen is "résume!"
So, "cliché" is in transition. In a few decades "cliche" will probably be the one listed first, and "cliché" the "alternate."