The invention relates to a fluid product dispensing device comprising: a body (10) a container (20) a dispensing head (100) including a dispensing port (5) and a dispensing member (30) such as a pump or valve mounted on the container (20) by means of a mounting ring (60). The dispensing member (30) comprises a dispensing member body (31) and a mobile member (35) that is moved axially in the dispensing member body when the dispensing member (30) is actuated. In addition the device comprises a lateral actuation system (40) which is solidly connected to the body (10) and which comprises an actuation element (41) that can move between a rest position in which the dispensing member (30) is not actuated and an actuation position in which the dispensing member (30) is actuated the above mentioned container moving in the body upon actuation. The body also comprises a sleeve (15) positioned around one part of the container at a small distance therefrom and a resilient member (425) that co operates with the container in order to bring same into contact with a side of the sleeve (15) said sleeve (15) extending around a lower part (25) of the container (20) and said resilient element (425) co operating with the container (20) outside the sleeve (15).
