Right. Note that the trigger is that you hit with the weapon, not deal damage with the weapon.
I.e.: charge is the action. It consists of the steps: move, make basic melee attack, apply damage and/or effects. You may not take any actions after you charge (i.e.: after you've applied damage and/or effects).
However, the free action in this case doesn't happen after the charge action, it is an reaction which happens during the charge action (after the make basic melee attack step and before the apply damage and effects step). Technically, even these steps aren't atomic (for example, the move step actually consists of a number of discrete "move one square" sub-steps, each of which can be interrupted by an OA).
I guess arguably if something was a free action which triggered on "you deal damage", then you could get into the situation where the free action is taken after the charge action is resolved, but as others have pointed out free actions can be taken when it's not your turn, so I think the order in that case would be: charge action, attackers turn ends, attacker takes free action (triggered by damage dealt during previous charge action) during next combatants turn. Of course, then you get into the weird situation that end of turn effects may alter things such that it's no longer legal/possible for the attacker to trigger the free action...
It's possible what actually should happen is that the charge consist of the sub-steps: begin charge, move, make basic melee attack, apply damage and effects, end charge.
And the players turn looks like: begin turn, <perform other actions>, charge, end turn. Then the free action could happen after apply damage and effects, but before end charge rather than after charge and before end turn (which is prohibited by the charge rules)...