I have a fairly different view of what makes Fiora weak, as well as what her kit gives to her in terms of theme.
First, Fiora is weak because her PQWE make her a duelist, but her R makes her a team fighter. Second, she is weak because her itemization isn't dependent on one or two stats, it is dependent on more like 8 stats.
Lets talk about her abilities first:
Passive - Her passive is kinda neat, but ultimately much of its power is hidden and dependent on her ability to survive through other means first. Fiora gains a life regen buff for every attack she makes that stacks a few times. This means to get up to full life regen she needs to have a high attack speed, and have already been in the fight for several seconds. But there is an inherent problem with that. She is squishy. She becomes easily burst down and if that happens she basically loses any benefit for her, she is a melee ADC, not a full fledged fighter, but this ability makes her dependent on being a full fledged fighter. In order to have this ability contribute to her kit she needs to buy HP, Attack Speed, Armor and Magic resist. For a passive, that's a lot to ask. If you want to fix this ability, you need to remove the over time component, and just give her life on hit.
Q - This is Fiora's gap closer but that's really the only reason she has this ability. It isn't supremely about fencing, it has a fencing name, but the actual thing she does in combat is very not fencing. So thematically it could go. However, we're in super high mobility land, and so she needs it. Unfortunately this ability is supremely hard to use as an escape because she can only use it on enemies, so its not really providing her the mobility that she needs for re-positioning as a melee ADC. She cant just dive in and not die like other fighters. In order to do its job this ability needs AD, Physical Pen, Movement speed, and potentially cooldown reduction. In order to fix this ability she needs to have the first use of her dash not require a target. This way she can create a gap fairly alright, but she is still REALLY good at closing that gap. Doing this would make the ability much less dependent on Fiora's movement speed to ever be useful.
W - This ability is actually the single most troublesome in her kit. While the rest of Fiora wants to build AD stats, this ability wants to build AP, Magic Pen, and CDR. This might be fine on a Fighter who would want to use some of those stats anyway, but Fiora does not, it is only for this ability. That needs to change. This needs to be made an AD ratio, and physical damage. But why stop there? This ability has so much potential for cool. This ability is Fiora creating a parry and riposte situation. This means that she deflects the attack, and creates an opening for attack. If we want to thematically make her into the awesome fencer she is supposed to be, this ability could use a touch-up. First, we need to shorten the timing window. 1.5 seconds may not seem like long, but for the power we're going to place in Fiora's hands in just a moment, that's a lot. 1s will do just fine. Next, the ability should apply a mark to the target that is affected. The mark lasts for only 1s itself, but it refreshes the CD of Fiora's Q, and if consumed provides a stun that is .75s long. The idea here is that Fiora uses this ability for punishing her opponents for an ill placed attack, and that her superior training and timing as a fencer allows her to not only parry but to really make an opening for herself. Because of the added utility and overall damage that this would add to her kit, the damage on this ability would likely need to be nerfed, but not only would this separate the good Fiora from the great Fiora, it would also really mesh well into her "I'm the best fencer there ever was" theme.
E - This ability while thematically a little weak is honestly just fine. If the other changes I've suggested are made then this ability could be left alone, its already one of the largest steroids in the game.
My word count has run dry so I'll expand in reply.
