Well, if your intention is just to force your girlfriend to play a game you really loved then by all means... but don't be surprised if she doesn't feel like playing video games after a while.
I like FF VII. I'd even say I like VII more than IX, though playing through IX with a friend can be a lot of fun. So I'm not just shouting out favorites here.
IX is definitely a safer bet for women, in my experience. Think about it...
1.) Unless she already likes Sci-fi (which is usually more popular with men) the world of FFIX is more visually interesting... more stylized and colorful aesthetic, a kind of fairytale-ish world everyone is a bit familiar with, more polished character models, and way more cuteness (the part with Vivi in the beginning is probably the main reason why FF IX will forever be known as "the girlfriend FF." That shit is potent.)
2.) You can play the game in multiplayer. It's really awkward to hand someone a controller and expect them to play something on their own when you're more excited about it then they are. (Which will probably be true with any old videogame you're convincing your girlfriend to play.) If it's something you can both play together, it's more like she's along for the ride, and it's much easier to get into.
3.) Probably the most exciting beginning of any Final Fantasy. It's just a bunch of great set pieces, and full of adventure. A bunch of theives kidnapping a princess. A mysterious kid exploring a walled city. A couple of kids sneaking into a castle to see a play. A hilarious, silly play with a dramatic sword fight. A bunch of goofy bad guys out of Alice in Wonderland (on hallucinogens). A chase. A big escape involving a bunch of cutscenes. All these things layered over each other and converging at once.
I'm not saying VII isn't also an appealing game for women. I actually had a creative writing teacher in college who had only started playing video games in her 20s, but thought GTA 3 and Final Fantasy VII were by far the best games ever. Really, it has to do with each individual person's tastes. If you want someone to enjoy something, show them what you think they'll like most. If your girlfriend doesn't like any kind of fantasy or fairytale, then FF IX isn't a good choice.
In my experience, there are a lot of women out there who think video games are all guns, explosions, blood, and dark settings. If you show someone with those preconceptions something that is really colorful, something like a fairytale but not, you get a chance at surprising them with what they've been missing. And that's the unique magic of FF IX.
