If Fox were smart (and sometimes that's a big "if") they would put X-men on hold for a while and focus on other characters to develop in order to keep the rights. Continue with Deadpool, X-force, Gambit, etc. I'd love for them to try and replicate Deadpool's success. Find an obscure character, find a creative team that's passionate about it, make it for a low budget and see if it succeeds. Then after several years, ideally more than a decade, bring back the X-men with a vengeance.
In a perfect world the rights would revert to Marvel and X-men would appear at the end of Phase 4, but I doubt that'll happen. Fox is in way too good of shape with the X-men to give it up. I highly doubt a sony type deal could happen, I just can't picture Fox Studios ever giving up creative control. I would love a deal to be made where Fox funds the movie and Marvel makes it.
In either case the most important thing they need to do with a reboot is set up the world of X-men for success. Like Star Wars: The Force Awakens, You need to effectively setup the world, the characters, and be done well as a film. So that all audiences can't wait for the next one. They gotta do it right.
I've probably said this on here before, but I'll say it again. IF/WHEN they do opt for a reboot, I think the best course for sustained quality and expansion of a well built X-Men universe is for them to go to TV. I firmly believe they make the most sense being in that format. A cinematic/high quality show that allows for every character to breath and builds up story lines throughout. I'm talking GOT level production quality. Nothing cheap or half assed. I know a lot of legal/rights wheeling and dealing would have to go into that and that its a total long shot, but I think long run that's the way to go. There is just too many characters and too many stories that can't/won't get properly developed on film. 8-10 hours of a show every year can spread the wealth around. Plus you can set up companion series to go with it. Like an X-Force or New Mutants or X-Factor.
I wouldn't get my hopes up, I doubt Marvel would allow that, I have a feeling the current tv deal excludes prime members and teams. More importantly there's no way Fox would do a series that doesn't premiere on one of their channels (Fox, FX, FXX) which are not known for high budgets or evening having faith in series often canceling them before their time. And if you'd expect GOT level budget from network tv you're dreaming. HBO is lucky because they're a subscription based channel and can risk much higher profits and far more freedom. In fact GOT's budget has got to be record breaking, if it wasn't so successful out of the gate it would have been quickly canceled. Plenty of other high budget series that were critically acclaimed were canceled way too soon. I remember Rome was planned for five seasons but only got two because the show was just too expensive to make. Not way Fox would ever have that kind of production level, you'd only get AoS/Flash level of production.
Still it is a cool thought. I always felt Watchmen would have been fantastic as a 12 episode series on HBO. Maybe after GOT ends they'll look into a superhero property.