"What we have to watch?" Is not a full sentence, but merely a subordinate clause that we use within a longer sentence: “I wonder what we have to watch” or “That is what we have to watch.” If your intention is to ask a direct question, we need to use inversion: “What do we have to watch?”
Although the meaning of “have to” is modal, English does not consider it to be a “modal verb” in terms of the grammar structure. English modal verbs are defective, that is, they have no infinitive or participles and do not take S in the present tense 3rd person singular. One such verb is “must” (which also lacks a past tense) — it can have the same meaning as “have to,” although “must” is usually used for expressing a high degree of certainty, rather than necessity.
The verb “(to) need” has a similar meaning as “to have to” and is likewise not classified as modal in American English. However, it can still sometimes be considered modal in British English. Another such “semimodal verb” is “ought” (originally the past subjunctive of “to owe”).
The list of “modal verbs” is actually quite short in English. Here are the main ones, off the top of my head:
can, could, may, might, must, will, would, shall, should
EDIT: I should point out that I've assumed your statement was about a requirement to watch something, since you asked if "have" was modal. A completely different interpretation would be that "have" refers to your having possession of watchable media. The structure would be exactly the same, and it would definitely not be modal.