I'm not a lawyer, so take this with a grain of salt.
I don't even know if Floyd has a (legal) reason to file a suit, but my thought right now is that he should forgoe the appeal to the CAS and instead, file a civil suit against the LNDD and the Chatenay-Malabry lab. If I recall correctly, the burden of proof in a civil case is different from that in a criminal case, and I think that out of a jury of 12 reasonable people, there might be at least a few that would look at the procedural missteps, wacky test handling and such that took place and find in Floyd's favor.
This occured to me after reading Christopher Campbell's dissent, specifically where he says:
"These doping allegations can cause substantial harm to a human being financially, physically and emotionally. It can destroy families. If, from time to time, WADA's mission obligates it to inflict such harm, it should be obligated to get it right -- all of it. As athlete's have strict liability rules, the labratories should be held strictly liable for their failure to abide by the rules and sound scientific practice."