Eleanor will be the fourth storm to hit France this winter, following Ana, Bruno and Carmen.
Storm Carmen hit during New Year celebrations, killing one man when a tree fell on his car, cutting off electricity to thousands of homes and felling a 60-metre-high wind turbine in the western Vendée region.
Storm Eleanor is expected to be of "comparable intensity", according to forecasters.
But it will hit different parts of France, coming from Ireland and the North Sea towards the Channel coast and sweeping down towards Paris on Tuesday night.
The worst is expected to be over by Wednesday afternoon.
Although the north-east is expected to bear the brunt, Finistère in the far west has been placed on flood warning because of the likelihood of huge waves along its coastline.