Right answer:
quiere
Querer is an infinitive verb, the most basic form of verbs in Spanish because it doesn't tell us anything about the person who performs the action or the tense in which the sentence is taking place. So we need to conjugate this verb. The more simple tense is the simple present, hence quiere is the conjugation of the verb querer for the third person singular in the simple present. Finally:
Paco quiere ir al Club de Jóvenes