Just to be clear, you never get the chance to fight during the enemy phase (barring some hypothetical future fast event that lets you fight). It makes no difference what weapon you have or even if you have a weapon at all.
It might be confusing coming from the board game, where investigator and monster "fight each other" at the same time. Here, the investigators fight in their turn (with no penalty for failing unless there's retaliate or its engaged with someone else) and the enemies attack when provoked or during. Enemy phase.