The best way of getting around Paris is to use the Metro underground railway. Almost all major attractions are within walking distance of a station, and you can buy a card that gives you daily access.
Romantics may like to use one of the horse and carriage taxis that you can find throughout the city in order to see the sights in a relaxed and intimate way.
Taxis are freely available, although you should agree a price with the driver before setting off, as sometimes, the driver will give you a full city tour - and charge you accordingly.