Some things to think about...
1. Fox needs a not so distant future replacement "go to" character as Hugh's Wolverine is (ironically) aging out. Don't get me wrong, Hugh Jackman is still in amazing shape and can still pull off the character, and may be able to do it for a few more years, but a some point (relatively soon) either Hugh will be done with Wolverine, or he will age out of the role. The point is that they need another character that the general audience loves, and Gambit is a really good possibility.
2. These movies take a long time to develop. Looking at the plans, Deadpoll will release in February of 2016, X-Men Apocalypse will release in May of 2016, Wolverine 3 in March of 2017, and an unknown X-Men movie in July of 2018. In addition, allegedly there will be X-Force and Gambit movies, though the years are unknown. With these actors, not moving forward can be problematic. A currently popular actor or actress can become less so, or start to cost too much, or quickly age out of certain roles.
3. The more they can introduce a character before their own movie, the more familiar the general audience is with them, making them more likely to go see it. Gambit would effectively be the epitome of this issue.
4. Think about the Apocalypse stories. Who is normally involved? Mr. Sinister is commonly found in them. And Mr. Sinister and Gambit have a very important history that would play well on the big screen.
5. Think about characters that Gambit has specifically been paired with. The one that speaks to me the most is Storm, which was from the story when Gambit first joined the X-Men. Most of you probably remember this story, where Storm was de-aged and Gambit and she went up against the Shadow King:
Now I'm not saying de-age Storm or use the Shadow King, just that Gambit and Storm have a canonical older brother/younger sister relationship, so why not use that?
6. This movie-verse has effectively ruined a romantic relationship between Gambit and Rogue (she's with Bobby and she's in the OT) or between Gambit and Storm (She's being recast as 16 years old in 1983 or she's older in the OT). Ok, lets accept it. No romance between Gambit and Rogue or Gambit and Storm. Fine, lets move on then...
7. It sure looks like Fox's focus is going to be this new cast of characters in the First Class timeline. Look, if you're recasting Storm, Jean and Scott; then that's where you're going to focus your future movies. Especially if that timeline can include McAvoy's Professor X, Lawrence's Mystique, Fassbender's Magneto, Hoult's Beast, Peters' Quicksilver and of course, Jackman's Wolverine. If Fox was smart (which is questionable) then they would be planning to having numerous X-Men movies with this cast in the 1980's and 1990's. There are many good stories and this is a proven cast of very popular actors and actresses. If they get it right for Storm, Jean and Scott, and maybe also do a young Nightcrawler; then they have pure gold!
So look, if it makes sense to continue using this new First Class timeline cast (with young Storm, Jean and Scott) then it makes sense to use Gambit in this timeline. Fit him in and use Tatum's start power as another boost for ticket sales.
Setting him up well in this movie will set him up for a solor flick, as well as additional roles in future X-Men movies. He could effectively become the next Wolverine (maybe).
Use the relationships from canon that can be used. Have him do something for Mr. Sinister that will affect his relationship with the X-Men in the future. Have him act as an older brother figure for this new, young Storm. Why not use the thief connection between Storm and Gambit as well as the Egypt connection between Storm and Apocalypse?
Now I'm not saying that Gambit should be a main focus of this Apocalypse story, just that he should be more than a quick cameo. Really, he needs to be introduced to the X-Men (like using Storm as the way in) and by the end of the movie he needs to be with the X-Men (if not considered an X-Men in status). If this movie ends with the X-Men characters as follows, they'll be in perfect shape:
Professor X
Beast
Cyclops
Marvel Girl (or Jean)
Storm
Gambit
Nightcrawler
Magneto
Quicksilver
and maybe others (like Acolytes)
Mystique and others (like Destiny, Toad, etc.)
Imagine what they could do in future movies? How perfect would it be to have a new X-Man join in the next movie, one that could be a romantic character for Storm? That character could possibly be Forge?
Next they could go against Mr. Sinister and get into the whole Gambit betrayal stuff, or they could go to space with the whole Asteroid M story, or maybe it could be time to bring the Shi'ar into things, and you know that Starjammers would be amazing (do you think they fall under Fox?).
And Gambit could easily be set up for an origin type story, such as Honor Among Thieves with Bella Donna, the Thieves and Assassin guilds, the Tithe Collector, etc. It's a good origin story, that is not truly an origin story (since it takes place in the present, though gets into the origin), and the concept of the Thieves and Assassin's Guilds would translate well to the big screen.