Vicious Mockery is a cantrip, so it doesn't require a spell slot, regardless.
Enthrall, on the other hand is a second level spell. This would normally require a spell slot to cast. But, as it is stated in the trait description:
[...] When you reach 5th level, you can cast the enthrall spell once with this trait. You must finish a long rest to cast these spells once again with this trait.
There is no mention of consuming spell slots, which means that you can do it regardless of spell slots - you do not need to even be a caster to use this ability.
However, this does not allow you to cast these spells using Spell Slots (and the Bard- A trait granted to you by your race is different to your Spell Casting ability, granted by class. Additionally, norwhile the Bard may have access to the Vicious Mockery cantrip, neither Sorcerer classor Bard have access to thisthe Enthrall spell, regardless) - you would need to multiclass into another class that had access to it in their spell list.