You’d have a really odd looking axe.
Basically there’s two problems, first is the blade itself, the second is the shaft. With the blade, you almost never want your weapon’s only sharp edge pointing towards you. At a concept level, sharpening the outside isn’t really a great solution, but it might work as a quick emergency modification.
The issue with the shaft varies. A lot of actual farm scythes I’ve seen over the years have contoured handles, sometimes even with separate fore grip setups. These are designed to make it easier to use the scythe in a repeated horizontal harvesting motion, but seriously limit the utility of one as a weapon.
I have the weird thought (and this is just speculation) that the simplest fix to re-purpose a scythe would be to actually reverse the blade, so it hooks away from the user. It would add a little more range, and might have some utility in catching and injuring incoming infantry. But, even that would also, probably ,fall into the category of some kind of emergency improvised weapon.
Strictly speaking, the issue isn’t just the scythe having a blade pointed towards the user. That’s also true with the kama, which, coincidentally, was also used to harvesting tool. It’s those contoured shafts that will mess you up.
Can you kill someone with it? Yes. But it’s a weapon of desperation, like a claw hammer. It shouldn’t be a professional soldier’s weapon of choice in any era. There will always be better options. Even if it’s just using a pitchfork as an improvised polearm.
It’s worth pointing out, there is a weapon called a warscythe. These had a curved scythe like blade, but it’s blade was fixed to be parallel with a normal straight shaft, rather than a normal scythe’s perpendicular construction. These were used (as far as I can tell) with normal thrusting and chopping motions.
The only thing the scythe is really good at (aside from harvesting grain) is looking really ominous. If your character is some kind of supernaturally empowered grim reaper, it’s a fine choice, physics be damned. But in something more grounded, the scythe is an emergency fall back for your villagers, after they’ve run out of torches and pitchforks.