Learn French: Je complète une phrase avec un mot. - I complete a sentence with a word.

This is a stem-changing verb. For verbs ending in -é_er like compléter, the é changes to an è in the present tense for the subjects je, tu, il/elle/on, and ils/elles. This change happens to match the natural spoken rhythm of the word when the ending is silent.

Do the nous and vous forms of this verb also use the è?

No, they keep the original é from the infinitive. We say nous complétons and vous complétez. Because the spoken emphasis is on the ending (-ons or -ez), the stem doesn't need to change its accent.

Is une phrase a false friend? It looks exactly like the English word "phrase".

Yes, it is a very common false friend! In French, une phrase means "a sentence", complete with a subject and a verb. If you want to say "a phrase" in the English sense (a small group of words), you would use a word like une expression.

Is the t at the end of mot pronounced?