Se foutre is a defective verb. It can not be conjugated in all possible forms.
Here are several examples of defectives verbs:
paître.
The verb
foutre. In grammar, a reflexive verb is, loosely, a verb whose direct object is the same as its subject, for example, "I wash myself". More generally, a reflexive verb has the same semantic agent and patient (typically represented syntactically by the subject and the direct object) are the same. For example, the English verb to perjure is reflexive, since one can only perjure oneself. In a wider sense, the term refers to any verb form whose grammatical object is a reflexive pronoun, regardless of semantics; such verbs are also referred to as pronominal verbs, especially in grammars of the Romance languages. A reflexive verb is always conjugated with a reflexive pronoun. Here is the list of the french reflexive pronouns:
« me »,
« te »,
« se »,
« nous »,
« vous »,
« se ».