Learn French: Il cherche quoi sous la table ? - What is he looking for under the table?

In everyday spoken French, it is very common to keep the normal statement word order and put the question word exactly where the answer would go. Because you would say Il cherche une boîte (He is looking for a box), you can simply ask Il cherche quoi ? (He is looking for what?).

Why use quoi for "what" here instead of que?

When the word for "what" comes after the verb in this casual question style, you must use quoi. The word que is only used when "what" is placed at the very beginning of a question.

Where is the word for "for" in this sentence?

The French verb chercher means "to look for" all by itself. You never add an extra word for "for" (like pour) after it. Therefore, il cherche already translates entirely to "he is looking for".

Why don't we say something like Il est chercher to mean "He is looking"?

French does not have a continuous "-ing" tense like English does. The present tense il cherche covers both "he looks" and "he is looking".