most people use sheds or playhouses outdoors or dog crates indoors. dog crates are better because of the giants height, it enables them to periscope which a "normal" rabbit indoor cage wont. You can also add a shelf for them to hop up and down on. I would warn you though if you are thinking of pens, the 4 frenchies I know and love will jump well over 5ft so you may be better off completely bunny proofing a room for them
Having slept with bonding bunnies before i would say my bunnies tend to:
3am - 7:00am - very active
7:00 - 9:00 - slightly active
9:00 - 5:00 - snooze time, although they will get up if something interesting happens
5:00 - 7:00 - slightly active
7:00 - 11:00 second snooze time, watching eastenders etc - no idea why
11:00 - 3 am - slightly active