This wouldn't be so much a class as a pair of weapons you could choose instead of the rifle/smg/shotgun.
For a primary weapon, it needs to be something relatively weak so that the medic should need to rely on a teammate or two for protection, but it needs to be a viable weapon if the medic is stranded and trying to get back behind friendly lines. So, I was thinking they should have a revolver: a seven shooter. It shouldn't be incredibly accurate, but neither should it be incredibly inaccurate, and it should probably have minimal recoil and a rate of fire only slightly higher than that of the shotgun's. As the name would imply, the revolver would have seven shots to a clip, and should have a reloading style similar to the shotgun's. I'd say the bullets should be around smg damage(25 body/75 head).
Now, as to how the medic would go about being... well, a medic, I should think that their grenades would be replaced with syringes or some other item that is readily associated with medicine. The Medic would have maybe 5 or 6 syringes. A syringe would heal a player to full health on primary fire, and heal the medic to full health on alternate fire. In addition, the medic may revive players who have not yet respawned by using a syringe on their corpse. A player who has already been revived once would not leave a body upon death, and medics would not leave bodies at all.
I don't think this would be too terribly overpowered with only 5-6 syringes per spawn/resupply, and in my opinion this game has always been in need of some way to regain health without dying&respawning or going all the way back to base.