Personally, I turn down weddings as I am not comfortable enough doing them. Have I done them? Yep. Similar to your situation, best friend pleaded for me to shoot her daughter's wedding. Ridiculously dark hall, used flash on a stand to bounce light around. Not the best pictures but in the end they loved what they got because the alternative would have been no pictures.
Like you, I also have a 6D and a 7D. I tend to do a lot of outdoor events and put my 24/70mm on my 6D and my 70/200mm on the 7D. The crop sensor gives me a little extra reach on the long end while the full frame utilizes the wide angle effectively. In your situation I would consider experimenting with the opposite setup (6D with 70/200 and 7D with 24/70) just because you will be in a much tighter environment and won't need that extra reach the crop sensor will give you with the long lens. If you're using the 35mm the 7D will give you a bit more as well. Play with all those combinations in your house ahead of time so you can feel out each lens/camera combo's reach. By the way, both cameras take the same batteries, so you're good there. Bring your charger(s) with you.
As people have noted, things move fast during a wedding and the last thing you need to be doing is fumbling with gear. The more comfortable you are with it the better it will be for you. Years ago I was a wedding DJ so I was comfortable with the routine. If they have a DJ I suggest introducing yourself as the DJ sets the pace for the sedding and can give you heads up as to what's happening next. Personally I talk to DJ's, wait staff, maid of honor/best man or even the parents. I never bother the bride and groom unless it's time for the formals.
You'll need to work effectively, not fast. If you try to rush things that's when problems will arise. Definitely take people's advice here and practice ahead of time. Knowing your settings (in relation to subject distance) will make things go smoothly with your flash work. Bounce that light always. Balance it with your ambient light. Gel it to match the venue.
Take multiple shots of everything. You will be surprised how many closed eyes, half open eyes, movement blur, awkward photo bombs in the background and countless other stupid issues happen as you're taking photos that you won't notice until you get home. Having alternates and seconds to use to fix things helps a great deal. You may have taken a 1000 shots, that doesn't mean you have to deliver 1000.
Take this lead time to browse through wedding photos online to get ideas. Print out the ones you want to create for your wedding party and have them handy as a reference. Don't rely on memory. Your memory WILL fail you the day of the wedding. I second the notion of having a contract. CYA!
Most of all, don't stress the little things. Know there are just some things out of your control.
Enjoy, have fun and use this as a learning experience.