Fluid dispenser device comprising a body (1) provided with a dispensing orifice (2) and a piercing element (4), said body (1) containing a reservoir (10) containing at least two doses of fluid product, said reservoir (10) comprising a proximal axial opening closed by a membrane (30) and a distal axial opening closed by a piston (20), slidably mounted in said reservoir (10) to distribute a dose of fluid product to each actuation, said reservoir (10) being axially movable with respect to said body (1) between a rest position, in which said piercing element (4) does not pass through said membrane (30), and a dispensing position, in which said piercing element (4) passes through said membrane (30), said membrane (30) being adapted to close in a sealed manner after each actuation, when said piercing element (4) emerges from said reservoir (10), said device comprising a system action lateral element comprising an actuating member (50), movable laterally relative to said body (1) between a rest position and an actuation position, said actuating member (50) being elastically biased towards its rest position, said actuator (50) comprising a first cam (51) cooperating with said reservoir (10) and a second cam (52) cooperating with said piston (20), so that the movement of said actuator (50) ) towards its actuation position first moves said reservoir (10) to its dispensing position and then slides said piston (20) in said reservoir (10), to dispense a dose of fluid. "Figure for the abstract: figure 2" Dispositif de distribution de produit fluide comportant un corps (1) pourvu d'un orifice de distribution (2) et d'un élément de perçage (4), ledit corps (1) contenant un réservoir (10) contenant au moins deux doses de produit fluide, ledit réservoir (10) comportant une ouverture axiale proximale obturée par une membrane (30) et une ouverture axiale distale obturée par un piston (20), monté coulissant dans ledit réservoir (10) pour distribuer une dose de produit fluide à chaq
