^ Not saying he has to by any means, but hear me out...
Yes, the characters in Avengers were all introduced singularly and then brought together as a team, but for the most part, that is not how the X-Men have worked (per canon). See, for the members of the Avengers, each were established (for the most part) as solo characters first, and then brought together, just like in the movie. The X-Men are, for the most part, younger characters brought together to be a team, and to learn how to use their powers. This is a bit different than the Avengers, or some of the other teams.
Yes, there are plenty of X-Men who were first established and then brought into the X-Men fold. Wolverine is a great example. But in the movie, since the draw for these movies is the X-Men tag line, Wolverine was first extablished IN an X-Men movie. The same should, IMO, happen for Gambit. Again, like others have suggested, it could be a cameo, or an after credit's scene, but why not use him in the movie?
Why not extablish him as an "X-Men" character before having his solo film?
Is Gambit known for being a solo character? A loner? Sure, but he's mostly known for being a member of the X-Men. So why not do that in the movies as well?
Put him in the X-Men: Apocalypse movie. Have the movie end with him being "part of the team", just like Wolvie was at the end of The X-Men#1, but he must leave and take care of some personal business, but "I'll be back soon, chere". He can then go off and deal with the whole Thieve's Guild and Assassin's Guild stuff, as well as Bella Donna, etc. And in that film we can learn about his origin and possibly his shady past.
This makes much more sense...
Let the GA get to know him before coming out with a solo film.