Arsenal striker Giroud, playing in his favoured central forward position, struck twice before the interval and once in the second half to lead France to an emphatic victory in Rennes.
Moussa Sissoko and Antoine Griezmann added goals in the last 15 minutes.
France are top of World Cup qualifying Group A and three points ahead of Sweden before they travel to Stockholm next Friday.
Giroud volleyed home from Ousmane Dembele's volley in the sixth minute.
He doubled the tally seven minutes later with a diving header after being perfectly set up by Dimitry Payet and he made it 3-0 in the 69th to become the first France player to score a hat-trick since David Trezeguet in 2000.
Giroud was replaced in the 73rd minute by Alexandre Lacazette and the Olympique Lyonnais forward had an immediate impact, finding Sissoko who tapped in from close range.
Griezmann completed the rout after a blunder by the Paraguay defence.
(Reporting by Julien Pretot; Editing by Ed Osmond)
