Give the reasons why you weren't into the franchise, and how you got into it. I'll give two examples of my own.

Grand Theft Auto: This was a series that I couldn't get into, mainly because my parents would not let me play it (it seemed to be the only game they wouldn't let me play), so I kind of envied the game when I heard others talking about how good it was and I wasn't able to play, to the point where I bashed the game to myself. However, not that I'm 17 I can play the game and the games actually look fun to me, and the storylines seem interesting to me.

And an even bigger example for me.

Resident Evil: I first saw others play Resident Evil 5 and 6, and I didn't get into the game. I wondered what the talk about it being creepy was. That waws until I saw gameplay for the PS1 Resident Evil games, and soon, I really started liking those games and now I am waiting an Asian import for the physical Resident Evil HD Remaster, and want to play the other games after.

For me, that's probably Phoenix Wright Ace Attorney because of my backlog

Always wanted to play it, but never really did until now

Persona, Infamous and Dragon Age.

Umm I'm hoping to add mass effect and Uncharted to this list as I've not tried either yet.

Otherwise I can't really think of anything.

Animal Crossing and Pokemon. I never was really interested in those series, but I bought New Leaf and Y version on impulse in 2013. Now I know I'm getting every new main series game in the series that isn't a spinoff or remake.

Monster Hunter. I'm like a crack addict with that game. My buddy had it on the PSP way back when I was like, "meh".  It sounded like a weak mmo with grinding rare drops at the time.  Now I get it, the gameplay is just too fun

Assassins Creed, I gave 2 and 3 a go never got hugely into it, Played Black Flag a bit never got hugely into it. Didn't come close to completing those 3.

But Unity just captured me, the city was huge and expansive the running in and out of random buildings was fantastic and the animations were varied and awesome. May have been a technical fuck up but I enjoyed that game very much.

Pokemon, I though it was crap until I played it.
Now it's my favorite franchise, lol.

animal crossing and fire emblem, i love those now. 

I think I might be getting into Street Fighter, though at this point it's more pure interest, I'm not yet sure if I'll get the game. I signed up for the beta, I hope I'll get in.

Street Fighter V's artstyle just speaks to me more than past games, at least in its current state, which I hope they don't change for the worse.