A fluid dispenser device having a reservoir; a valve; a cocking member movable between rest and primed positions and between primed and dispensing positions, the cocking member includes a set of teeth; a blocking device blocking the cocking member in the primed position; a trigger system controlled by inhaling to release the blocking device; a reservoir support element including a cam opening; and a meshing wheel having a toothed projection co-operating with the set of teeth and a cam projection co-operating with the cam opening. The toothed projection is centered relative to the wheel rotation axis, and the cam projection is offset relative to the axis. The meshing wheel completes a turn when the cocking member moves from its primed towards its dispensing position, such that the cam projection causes the reservoir support element to perform reciprocating axial movement for actuating and returning the valve into its rest position.