Sorcerer has very little to offer an Arcane Archer-type build, with the exception of the Elemental Affinity feature from the Draconic Bloodline origin. Combined with Elemental Weapon, this allows you to add your Cha modifier as elemental damage to every shot you fire from your crossbow. The problem here is that Elemental Weapon is restricted to the Paladin class only.
So you have 3 options, explained below. Regardless of which you take, you'll be focussing on Cha and Dex, with Con as a secondary as usual. So you'll want to spend your 27 points in the 15,15,15,8,8,8 pattern. Then Half-Elf brings you up to 17 Cha, 16 Dex, 16 Con very neatly. Each build gets you 5 ability score increases over your career. You'll want to use these to bring Cha and Dex up to 20 and take Crossbow Expert so that you can dual-wield hand crossbows.
Option 1 is to take at least 9 levels of Paladin so you can cast Elemental Weapon. Then you'll want to bring Sorcerer up to 8 and Paladin up to 12 so you don't lose ability score increases. This isn't a terrible idea, as many of the Paladin's [X]ing Smite spells work with ranged attacks, making a pretty reasonable Arcane Archer. With the Oath of Devotion's Sacred Weapon ability, you could also add your Cha modifier to your attack rolls. That said, many of the Paladin's class features don't work with ranged attacks, and it's not exactly an Arcane Archer anyway. Also, you'll have to have Str 13 to multiclass Paladin; so your starting ability scores will be 15,15,13,12,8,8 with Half-Elf making it 17 Cha, 16 Dex, 13 Str, 13 Con. (You only lose out on Con, so it's not too bad.) The main thing this option gets you that the other 2 don't is the cool Smite spells that add damage and additional effects to your crossbow attacks, just like an Arcane Archer.
Option 2 is to take 6 levels of Lore Bard for Additional Magical Secrets, which you can use to gain access to Elemental Weapon. You could use the other magical secret to get Branding Smite for that Arcane Archer flavour. Then, you'll want to take 5 levels in a martial class for Extra Attack; I'd strongly recommend Fighter, so that you can take Fighter 6 and not lose an ability score increase. Once you're Sorcerer 6/Bard 6/Fighter 6, take 2 more levels in whichever of these 3 classes you like to get your last ability score increase. This option is the least focussed, but you get the Archery fighting style and Improved Critical for your crossbow, so it's got a slight edge with the crossbow you're looking to optimize. This can also get you Arcane Archer-ing the fastest, since your combo comes into play at level 12.
The final option is to take 10 levels of Valor Bard, and use Magical Secrets to get Elemental Weapon. The other magical secret could be used for Banishing Smite, Branding Smite, or Staggering Smite for more Arcane Archer flavour. While this doesn't sound as good as Lore Bard, you get Extra Attack for free along the way. Then you should probably take Sorcerer up to 8 and Bard up to 12 to keep all your ability score increases. This option gets you the most powerful spellcasting of all of them, but you don't get the Archery fighting style.