I don't think giving Fiora CC is the answer to her problems.
When reworking a champion, Riot works hard to keep the original flavor and playstyle of the champion. Part of Fiora's playstyle is that she brings no CC to the table, just damage and mobility.
I'll give an example. When Riot reworked Kat, a lot of people were saying she needs CC to be viable, but Kat's lack of CC was part of her distintive playstyle. So she got reworked without CC and now she's been played in several major tournaments.
What I'm saying is that Fiora can be 100% viable without CC. Yes, a melee carry is a totally different beast than an AP carry (Kat). In my opinion, Fiora needs stronger defenses. A character that needs to build glass to be effective has to have built-in defenses in her abilities.
Jax is a good example of a character with built-in defenses. He can dodge all autos for a few seconds, stun in an area, and his ulti gives him a defensive steroid. As crazy as it sounds, Fiora needs more than that, but in different ways. For a melee carry like Fi to be viable, she needs some combination of defensive steroids, CC immunity, cleanses, shields, heals, blocks, untargetability, etc.
Riot has tried to do this with melee carries. Tryn has his no-death-period and a heal, Fi has untargetability and Riposte to block one auto, and Yi has Slow Immunity on his ult and defensive steroids/healing on Meditate. But the fact that none of these are viable on a tournament level should tell you that these defensive abilities are not enough. They either need more inborn defenses so they can live while building glass, or the class needs to be reworked entirely.
One last thing: note that no melee carry so far has strong CC. That's because CC pushes AD champs to be assassins or bruisers. Strong CC + burst build = assassin; Strong CC + tank/mixed build = bruiser. This means that CC is not the answer for melee carries. Instead, their kits should be distinctly anti-CC. They should counter CC, so to speak. This is the answer to the melee carry conundrum for Riot, and this is how they should think about melee carries as they eventually rework Tryn, Fiora, and AD Yi.