Spanish has no need of a separate future here. Either some future context in the sentence carries it, or you use ir a exactly as English uses going to.
voy a / vas a / va a / vamos a + "to" form
La semana que viene is worth unpacking: la semana (the week), que (that, which), viene (it comes).
Vamos a verla · ¿Vas a verlo pronto? · ¿Vas a vernos pronto? / ¿Nos vas a ver pronto? · ¿Por qué no vas a vernos pronto?
By the rule I see would be "vo", which was too short, so it became veo, v-e-o. Everything else is regular.
La veo más tarde · La veo esta noche · La vemos pronto · Las vemos pronto · Las ve pronto · ¿Las ves pronto? · ¿No las ves pronto? · ¿Por qué no las ves pronto?
Asked for we are seeing her soon, the student produces "la venemos". The correction is blunt and worth quoting: no guessing at all, it is the only rule.
Nos covers us, ourselves and each other, all of it.
Nos vemos. (we see each other)
That is a common way of saying goodbye in Spanish. The future context here is simply the fact that you are saying goodbye: nobody thinks nos vemos means you are seeing each other right now. The context is never even stated, and it still licenses the present.
Nos vemos la semana que viene · Hablamos la semana que viene (let's speak next week)
The "we" form doubles as let's, the way vamos does.
The student stalls holding a whole sentence in mind, trying to translate it. That process works when you are memorising, but this is not memorising: it is building.
hablamos · la semana · que viene
The student forgets viene mid-sentence. That is fine. Every time you find it again, you strengthen the process, and the process is what you actually need.