It has pretty much been confirmed up to this point that Titanfall, at least the first game in the series, has been announced to be a Microsoft exclusive. This means that it will only be available on Microsoft platforms.
So far, a release has been set for the Xbox 360, Xbox One, and PC, and although many Microsoft representatives have already stated that it will be a lifetime exclusivity, many others aren't so sure this is the case.
One of the main reasons why I personally doubt Titanfall will stay on Xbox for the duration of it's lifetime is because EA have too much of a good chance to bring in both a huge revenue, and a massive player base if they aimed for the PlayStation 4 as well as the Xbox One.
So, unless Microsoft are paying a heavy load of money EA's way, I'd say it's very likely that future Titanfall games will be cross-platform.
I'm not the only one that believes this either. In fact, Sony Computer Entertainment Europe Brand Manager Alex Moyet tweeted out to say that she too believes that it won't be long before Titanfall is moved over to cross-platform status. Her tweet was in reply to another twitter user and said,
"Nah we might have to wait another year or so but I've got a good feeling it'll come to PS4."
Although her tweet has since been removed, the internet won't let such a piece of information slip into the unknown. Her reply was short and simple, but it certainly got a point across.