Totally agree, a simple walk around will help you get your bearings.
Try starting at Les Invalides and then walk to The Effiel Tower, Arc de Triomphe, Champs Elysees, Place de La Concorde, Louvre, Hotel de Ville and finish at Notre Dame. It's a cracking walk and takes in alot of the attractions...
If you want romance you've picked the right place. A romantic jesture that the good lady wife loved was writing our names on a padlock attaching it to the railings on the Solferino footbridge and lozing the key in The Seine.