I believe the lowest that is recommended is about 30-36″. I don’t think most Flemish Giants are high jumpers though so hopefully someone that knows more about them will comment.

As long as he doesn’t eat the plastic I don’t think it should be huge problem. Another option would be to get a large, cheap, piece of vinyl flooring. If you have a Home Depot near you they may stock this or something like it:
http://www.homedepot.com/p/Armstrong-12-ft-Wide-Royelle-Sheffley-Black-and-White-Residential-Sheet-Vinyl-61338405/100157067#.UeYFto1JP4s

You could get enough for two x-pens for under $20.

Another member called around to discount carpet places and ending up getting some sheet vinyl for free I believe. You might find a good deal on something similar on craigslist 

My only experience with bunnies is my current holland lop and we have him in a 36″ xpen. I’m sure shorter would’ve worked fine as he isn’t a jumper. You might want to go taller especially if you’ll have a hidey house or cardboard box or something in the pen that he could potentially hop on to help him escape. Our xpen has a door which I highly suggest. Even though it is too tall to reach over and into comfortably, we just open the door to clean, change litter, etc. We also got a remnant piece of vinyl from Home Depot as a floor. You could always try something like that over your carpet. It is easy to clean – any spilled water or urine accident doesn’t soak in and wipes easily.

As the Mom of a 3 month old flemmie – let me tell you that mine jumps the 30″ baby gate! And not only does she jump it, she does this from floor level while the gate is up on the first step of the stairs we were trying to block! Each bunny is different, but my flemmie is a determined little cuss and easily jumps quite high. We used an XXL dog crate to litter train her, which she obviously could not jump out of. now she has the run of the house. . Good luck!!