I'm playing with the idea of a Human Draonic Linage Sorcerer, probably focusing Fire Damage spells. But I also like he idea of having a secondary focus of being able to fight in melee with claws as his main weapon. I'll need to get my DM to let me use the Dragon Hide Feat for my starting one to get the weapons. Just looking for any suggestions on multiclassing, how to be optimize this build etc.... 

In short - Vulcan crossed with Sabretooth from X-Men.

Any help or suggestions will be appreciated, Thanks in advance 

Well, claws certainly wouldn't be a bad thing early game. The only issue is that their damage is pretty small and doesnt scale.  If you want to have a strong melee presence, it would probably be worth picking up some buff spells for yourself and making sure your Con score is high enough to succeed concentration checks. If you like the idea of dealing high damage with your draconic claws, you could probably pick up some melee spells/cantrips and simply reflavor them to look like claws extending from your hands as long as it makes sense.

The overarching issues that can't be solved too easily with spells is that your melee presence will be weak. The claws only do a d4 of damage and you don't get extra attack as a sorcerer. 

You're going to need to roll WELL for your stats to make that work, I think. Your spellcasting will rely on Charisma, your AC will rely on Dexterity, your claw attacks will rely on Strength, and as a Sorcerer you won't be overflowing with Hit Points so you'll probably want decent Constitution as well. Instead of taking Dragon Hide, you could take a level of Fighter which would get you medium armor proficiency(heavy if you start as a Fighter at Level 1), and in the new Tasha's Cauldron book coming out soon there's an Unarmed Fighting fighting style option which I believe lets you make unarmed strikes for 1d6(1d8 if using both hands, though I think they tweaked the wording on that part). Also in Tasha's, it looks like Primal Savagery is getting added to the Sorcerer spell list. This would offer a similar roleplaying effect as unarmed strikes, but would key off Charisma instead of Strength, and the damage would scale up with your level. If you were willing to multiclass more than one level, you could take 3 levels of Path Of The Beast Barbarian, which would give you the choice of a bite, claw or tail attack whenever you rage(though it would also mean attacking with Strength).

Your idea is intriguing, but Sorcerers are difficult to build as melee combatants. Wizards has tried more than once to make a Sorcerer Bloodline good for melee(Stone Sorcerer and Giant Soul Sorcerer), neither one worked out.

The Blood Hunter (Lycan) would be one very straightforward way to build for this, as that class' Crimson Rite can give your character claw attacks with bonus fire damage on them. 

A different Blood Hunter subclass + a race with a natural weapon (such as Dragonborn[with dragonhide feat], Lizardfolk, Tabaxi, Leonin, Aarakocra, Tortle, Centaur, Minotaur, Simic Hybrid, or Shifter) would also be a way to enhance that racial natural weapon with fire damage. 

Or, a Monk + Blood Hunter multiclass. Or, a Blood Hunter + Sorcerer. Or, lots of stuff.

Alter Self can also provide you natural weapon claws for quite a long time, though as a concentration spell it will interfere with other defense  or fire damage buffs and risk dropping all the time.

Really, the Blood Hunter seems to me like the most straightforward way to achieve elemental claws. They are quite a MAD class, wanting Strength/Dex, AND at least a middling Intelligence, AND probably constitution... not even to mention AND your Charisma focus, if you want to multi Sorcerer... but that being said, they play with fire well, and a Blood Hunter (Profane Soul) or (Ghostslayer) can make a pretty effective pyromancer brawler all on its own.