The keyword to learn to talk about being in a relationship is the masculine noun couple.
For example, to say that you’re in a relationship with someone, you can use the expression être en couple.
Ils sont en couple depuis deux mois.
They’ve been in a relationship (or: they’ve been together) for two months.
J’ai un kick sur toi, mais je suis en couple.
I’ve got a crush on you (or: I’ve got the hots for you, I really like you), but I’m in a relationship.
To say in our relationship, you can use dans notre couple.
On a des problèmes dans notre couple.
We’ve got problems in our relationship.
Pronunciation tips:
In ils sont en from the first example, the word en is in fact pronounced t’en because of the liaison. Also, colloquially, ils contracts to i’. This means ils sont en sounds as though it were written i’ son t’en.
In the second example, je suis en can be pronounced colloquially as though it were written ch’t’en, where je suis contracts to the French ch sound (like in chaise, cher, etc.). A t then comes in between the contracted ch sound and the word en: ch + t + en, said all in one syllable (chten). You’ll discover and listen to many more contractions like this in Contracted French.
