Probably not. The 8240 is a very low end onboard GPU and really doesn't meet the minimum requirements for this game. You can find the system requirements here: http://na.finalfantasyxiv.com/heavensward. Have you been able to play the game with higher FPS before?

If you have a PS3/4 you can play there, otherwise you'll probably need a new PC to get any sort of playable performance.