Heya,
At 10 feet, 50mm will be a near half body shot. 85mm will get you face portraits.
This is where a 70-200 would be quite important.
The 6D can handle shooting at ISO 12,800 in RAW, expose slightly to the right so that you can work the noise later in post. Shutter speed in low light at F4 should be doable even at longer lengths.
I'd take the 85mm if you already have it.
If you're getting a lens, I wouldn't take a 24-105F4L without flash to something like this. If you're going to spend that kind of money on a F4L lens, buy a 70-200 F4L instead. Make the big lens worth it by having way more options in case you're not just 10 feet away.
Flash would be really ideal.
But the 6D should be able to handle it. But I would still take the fastest glass you can.
What kind of shots are you wanting? Face? Bust? Full body? If you want all that, a zoom sounds right. But if you know you just want bust/face, a long fast prime would really give you awesome results. But in such an uncontrolled environment, a zoom would probably be better for you.
Can't help but think about the Tamron 24-70 F2.8 VC. Or even a simple 28-75 F2.8 Tamron. Every stop of light counts even on the 6D when you can't use flash. Unless you can afford a 70-200 F2.8 of some flavor (Tamron's 70-200 F2.8 VC is affordable and awesome).
Very best,