A fluid dispenser comprising a dispenser member (1), such as a pump, a dispenser head (14), such as a fluid applicator, and a fluid reservoir (2) that is connected in leaktight and removable manner to the dispenser member (1), the fluid dispenser being characterized in that the sealing between the dispenser member (1) and the fluid reservoir (2) is obtained by coaxially sliding leaktight radial contact that is interrupted when the fluid reservoir (2) is disconnected from the dispenser member (1), such that the fluid reservoir (2) is connected in leaktight manner to the dispenser member (1) over a determined axial height range.