TLDR: Battlefield 4 is beautiful, but was not made for kids. There are lots of beautiful FPS (First Person Shooters) out there without the same level of violence, profanity, and uncanny realism. (I would recommend the latest iteration of Halo, which has traditionally favored a younger audience.)
The battlefield franchise (particularly bf4) is popular because it represents the cutting edge in graphic realism. A fire burns like a fire, smoke rises like smoke, and when boxes explode, papers go flying.
If you have a nice system, it's a very gratifying experience. The game-play is immersive because it never breaks character - it's not cute or quaint, it looks and feels real. (When you look down, you have legs. When you jump a barrier, hands reach down to lift you over. When you swim, you swim. When you shoot the terrain, it changes accordingly.)
The game isn't deliberately gory - you won't find bits and pieces of people floating around. But the game doesn't sugarcoat things either. BF4 is intended for adults - so you'll see blood and not confetti when you shoot, knife, or shell an enemy. The cut scenes and scenarios in the campaign (single player mode) are particularly unsettling. (But more tasteful than the Gears of War or Deadspace series.)
As for language, I felt like the campaign swore a lot more than your typical rated R film. (Again, the idea being that men at war would actually speak this way in an emergency.)
If you would like your children to play online, be aware that the good majority of players your child will be interacting with are adults.
I'm not of the camp that believes violent videogames will turn children into violent people. That said, BF4's commitment to realism means that the true-to-life video effects can be unsettling for younger participants. If you feel that your children are particularly impressionable (or would like to protect their eyes and ears from a game geared towards adults,) you'd be better off purchasing a different FPS (First Person Shooter.)