"She is looking for her cat."
Translation:Elle cherche son chat.
"cherchant" is the present participle of "chercher".
we don't use it often, and especially not to translate the English continuous tenses, which do not exist as verbal forms in French.
So, if you get "she is looking for her cat", you translate either with simple present: "elle cherche son chat" or with "elle est en train de chercher son chat", where "en train de + infinitive" correctly translates the idea of an ongoing action.