Goliath Barbarian, Berserker; level 10+
Let's start off with the race; Goliath. I know you wanted human, but as far as I'm concerned, Goliaths are a spiritual subrace of humans. Tall, northern, tough, barbarians (little 'b'). +2 Strength and +1 Constitution are a great start and the other bonuses are gravy, not to mention that they're "acclimated to cold climates".
I think his starting array should be 14,10,15,8,13,12; that nets us:
- Strength 16
- Dexterity 10
- Constitution 16
- Intelligence 8
- Wisdom 13
- Charisma 12
His class is obviously going to be Barbarian (big 'B'). As much as I am loathe to say it, I think Berserker is the right fit here. The Mindless Rage feature grants a hefty benefit against charm and fright. Then at level 10, you get Intimidating Presence.
We can be done here. The character is online at level 10. But, let's try to check some other boxes and I'll give my recommended 20 build at the end.
Incredible Strength and Constitution
Our Fafhrd can have 20 Strength and 16 Constitution at level 10. That's not bad. If you want 20/20, you'll have to go to level 16. If you want higher than that, you'll need to get to level 20 and unlock the Barbarian capstone Primal Champion to break into 24/24, which are truly extraordinary.
Inflicts more damage per blow than most fighters
Again, Barbarian is a big help here. Added damage to every attack, plus Brutal Critical for when you manage a 20 gives you extra dice. Specifically for 1-handed attacks, you might want to consider a Fighter dip, but I'll talk about that later.
Using a two-handed sword in one hand
There's no precedent for this. You've got a few options, and I'm not sure you're going to like any of them.
You can homebrew a feat to let you use versatile weapons one-handed and gain the bonus; probably also gain +1 Strength.... and ... it'd need something else to be competitive.
The Unearthed Arcana feat: Blade Mastery. Average damage on a longsword in two hands is 5.5, vs 4.5 of one-handed. Add in the +1 damage from the feat and it feels a lot like you're using a longsword with two hands. Not perfect, but something. (and it gives a couple other bonuses)
Use the sword two-handed, but say it's one-handed. This is my preferred option
Fighter dip to snag the dueling style, which grants +2 damage when you're holding a one-handed weapon and no other weapon. This synergizes well with the Champion archetype and does fun things with crits. This is my second favorite option
Your DM might veto this, but I don't see why and as far as I understand, it's RAW.Have Fafhrd wield a large longsword, with disadvantage. It'd deal 2d8 damage, which is pretty cool, and you can reckless attack to negate the disadvantage. If you fighter dip with this option, I recommend Battle Master instead of Champion to improve your to-hit.
A creature has disadvantage on attack rolls with a weapon that is sized for a larger attacker. You can rule that a weapon sized for an attacker two or more sizes larger is too big for the creature to use at all.
Use reaction against opponent's attacks
Berserker gets this baked in at level 14. Done and Done. Battle Master Fighter also gets access to this. More attacks is more better.
Win Initiative and difficult to surprise
Again, Barbarian has it already baked-in.
By 7th level, you have advantage on initiative rolls.
Additionally, if you are surprised at the beginning of combat and aren't incapacitated, you can act normally on your first turn, but only if you enter your rage before doing anything else on that turn.
If you've got a spare feat, you can take Alert, but it's optional.
His appearance can be whatever you say. Charisma does not equal comeliness. It's a factor, sure, but they're not the same.
If you want to score more critical hits, either have advantage, and/or take three levels of Champion Fighter.
If you want to have "battlefield maneuvers", you're going to have to have the Martial Adept feat, or you're going to have to take a Battlemaster, which is mutually exclusive with taking Champion, as mentioned above.
Hand axe and dagger are easy to deal with, but "reasonably good with a bow" is subjective and going to be difficult with our build. Honestly, I think it's fine as-is, but if you want to be a master archer, then you're going to have problems as a barbarian.
Build and Closing Thoughts
You need to decide if you want the Barbarian capstone or not.
That's the only real decision as far as I'm concerned. If you're fine without it (I am), I would use Barbarian (Berserker) 17 / Fighter (Champion) 3; grab the Dueling style. This gives you Brutal Critical (3) and Improved Critical so that you roll three extra dice on a crit, which happens on 19-20. This leaves you with only 4 ASIs, which you're going to pump into Strength and Constitution (no room for feats). Don't worry, in exchange you'll get a longsword attack +12 that deals 1d8+11 damage and crits for a total of 5d8+11 (about 20% of the time, if you have advantage).
If you plan on using the longsword two-handed for that d10 damage, then take the Great Weapon Fighting style, which will also help out on those crits you're scoring every other turn (if you're reckless attacking and Frenzying).
The biggest hangup you're going to have is making the "using a two handed sword with one hand" feel good. There just isn't a good RAW option other than "keep using a two handed sword and say that you're using it with one hand". 5e loves reflavoring things; so who am I to argue. Otherwise, you're probably going to be in homebrew territory.