Beset by terrorist violence, the Paris of today is far different from the romantic image long associated with the city by the Seine. To recapture that aura, you will need to watch Woody Allen's Midnight in Paris (2011) or an older film that offers romance or intrigue. One such film is Under Paris Skies ("Sous le Ciel de Paris") from 1951 which features a song of the same name. In the movie, the fates of multiple otherwise unconnected characters intertwine under the sky of Paris in the course of one day.
The song was sung by Jean Bretonnière in the movie, but the more famous version is by Édith Piaf who recorded it in 1954. Other recordings were by Yves Montand, Mireille Mathieu and Juliette Greco. The song has long been a staple of French sidewalk cafes and cabarets, often accompanied by accordion.
For other French songs on my site, try "La Vie en Rose" and "The Poor People of Paris", all of them hits for Édith Piaf.