A stroll along Seine's waterfront is a must while in the City of Lights, no matter if you have a sweetheart or not. Many of the famous landmarks of Paris are located by the river (e.g. the Eiffel Tower or the Louvre) so you can use it for orientation too.
You can enjoy the river on tour boats or the hop on hop off boats, some operators offer even private dining experiences.
On the riverbanks, there are floating restaurants, cafés and discos. There are also many benches, where you can sit with your picnic and admire the views. The riverbanks are also popular among sunbathers, cyclists and joggers.
Wikipedia https://en.wikipedia.org/wiki/Seine
Address 4 Quai François Mitterrand, Paris 75001, France
Coordinates 48°51'34.602" N 2°20'7.418" E