Jeannette : Why don't you tell me what happened the other day? Jules: Ah nevermind, it's nothing important. Jeannette : Pourquoi ne me-dis tu pas ce qui s'est passé l'autre jour ? Jules : Ah laisse tomber, c'est rien d'important.

It depends on the context. If for example you you ask someone to do you something but then see it's easier to just do it yourself (or you ser by their reaction that they are bothered by your request), you could say "Non mais laissez tomber" (literally means "drop it", but in this context means "never mind, forget it").

never mind = pas de soucis / c'est rien

Ce n'est pas grave

There is no expression exactly covering "never mind" but you can say Oublie ça ! (forget it) Laisse faire ! (drop it) Ça fait rien ! (it's nothing) C'est pas grave ! (it's not important) Tant pis ! (too bad) instead.