The Chelsea striker, named as captain for the game at the Stade de France, was in fine form for the reigning world champion.
Eduardo Camavinga broke the deadlock in the ninth minute with an exquisite opener, before Giroud lit up the game with a stunning long-range strike 15 minutes later. He then made it 3-0 in the 34th minute, with Vitalii Mykolenko's own goal soon after putting the game beyond doubt.
Viktor Tsygankov reduced the deficit eight minutes into the second half but Corentin Tolisso bent home and Kylian Mbappe added a sixth before Antoine Griezmann's fortuitous effort rounded off a rout that thoroughly reflected France's dominance.
Skipper Giroud was involved as Camavinga marked his first start in spectacular fashion.
Georgi Bushchan did well to keep out Giroud's close-range header, but Camavinga was there to convert on the rebound with a deft overhead kick that looped beyond the forlorn Ukraine goalkeeper.
Anthony Martial was denied at the near post after a neat run into the box and Camavinga fired over with a long-range volley before Giroud ensured his landmark appearance would be a memorable one.
His perfectly placed left-footed effort left Bushchan with no chance, while there was to be further misery for the visitors.
Tolisso saw a half-volley tipped over but Bushchan was soon picking the ball out of his net again, the keeper only able to turn Houssem Aouar's long-range effort as far as Giroud, who doubled his tally with a diving header.
Ruslan Malinovskiy spurned a gilt-edged chance at the other end and that profligacy was punished as Martial was again thwarted by Bushchan, only for Mykolenko to head into his own net from the resulting corner.
Malinovskiy tested Steve Mandanda twice before the interval and Ukraine did get some reward for their efforts in the 53rd minute through Tsygankov's vicious drive.
Normal service quickly resumed, however, as Tolisso sent a sublime finish into the bottom-right corner after cleverly linking up with Mbappe, who eight minutes from time weaved his way into the box and rifled home.
There was still time for Griezmann to have the last word, his powerful strike taking a heavy deflection to leave poor Bushchan rooted to the spot.