A broadband seismological station (PRIMA) installed offshore Nice airport (southeastern France) reveals a strong amplification effect of seismic waves. PRIMA station was in operation for 2 years (9/2016 to 10/2018) on the outer shelf at a water depth of 18 m. Situated at the mouth of the Var River, this zone is unstable and prone to landslides. A catastrophic landslide and tsunami already occurred in 1979, causing 10 casualties. Given the level of seismicity of the area, it is important to infer the impact of an earthquake on this zone. We analyze the recordings of earthquakes and seismic noise at the PRIMA station by comparing them to nearby inland stations. We find that the seismic waves are strongly amplified at PRIMA at some specific frequencies (with an amplification factor greater than 10 at 0.9 Hz). Using geological and geophysical data, we show that the main amplification frequency peak (at 0.9 Hz) is due to the velocity contrast between the Pliocene sedimentary layer and fine-grained sediments dated from the Holocene, at about 100 m depth. This velocity contrast is also present along the Var valley, but the level of amplification detected on PRIMA station is larger. Using numerical simulations of seismic waves in a 2D model that accounts for the pinch-out geometry related to the termination of the Holocene sedimentary layer, we can partially explain this amplification. This offshore site effect could have a crucial impact on the triggering of a submarine landslide by an earthquake in this region. More generally, this effect should be taken into account for the modeling of landslides and induced tsunamis triggered by seismic waves.