Fluid product dispensing device

A fluid dispenser device comprising a dispenser member (10), such as a pump or a valve, a fluid reservoir (30), a fastener element (20) for fastening said dispenser member (10) onto a neck (35) of said reservoir (30), and a turret (40) disposed between the body (11) of the dispenser member (10) and said fastener element (20), the device being characterized in that said turret (40) includes a deformable radial flange (45), said deformable radial flange including deformable sealing means (46, 47) projecting from said radial flange (45), which radial flange (45), before assembly, curves upwards, and after assembly, is deformed and co-operates in leaktight manner with the top edge of the neck (35) of the reservoir (30), and which sealing means (46, 47), after assembly, are also deformed and co-operates in leaktight manner with said fastener element (20).