A fluid dispenser device comprising a body (10), a reservoir (20), a dispenser head (100) incorporating a dispenser orifice (5), and a dispenser member (30), such as a pump or a valve, that is mounted on said reservoir (20) by means of a fastener ring (60), said dispenser member (30) comprising a dispenser-member body (31) and a movable member (35) that moves axially in said dispenser-member body while said dispenser member (30) is being actuated, said device further comprising a lateral actuator system (40) that is secured to said body (10), said system including an actuator element (41) that between a rest position in which said dispenser member (30) is not actuated, and an actuated position in which said dispenser member (30) is actuated, said reservoir moving in said body during actuation, said body including a sleeve (15) that is arranged with a small gap around a portion of said reservoir, said body further including a resilient member (425) that co-operates with said reservoir so as to urge it into contact with a side of said sleeve (15) of the body, said sleeve (15) of the body extending around a bottom portion (25) of the reservoir (20), said resilient element (425) co-operating with the reservoir (20) outside said sleeve (15).
