No, you can’t improve an existing melee attack with the Vampiric Touch
The Vampiric Touch spell states:
The touch of your shadow-wreathed hand can siphon life force from others to heal your wounds. Make a melee spell attack against a creature within your reach. On a hit, the target takes 3d6 necrotic damage, and you regain hit points equal to half the amount of necrotic damage dealt. Until the spell ends, you can make the attack again on each of your turns as an action.
So, firstly you take the Cast A Spell action and expend a 3rd level spell slot. Then you deal 3d6 necrotic damage, if you succeed with the melee spell attack. This melee spell attack is a part of the spell — you literally have to touch the target with “your shadow-wreathed hand” to apply the spell effect.
Within 1 minute, you can repeat this action without expending more spell slots, providing you maintain the concentration. So you have to choose — either you make a weapon attack with your pact weapon, or you make a spell attack with the Vampiric Touch.
See also Can you apply the Vampiric Touch and Shocking Grasp damage together in one attack?