President Francois Hollande was in the stadium but was rushed away as blasts were heard near the venue north of Paris.
The French, missing the injured Karim Benzema and Mathieu Valbuena following a sex-tape scandal, had to wait until the stroke of halftime to make an impact with Giroud continuing his fine scoring run this season by slotting the ball in from an Anthony Martial cut-back.
Gignac headed the second goal in the 86th minute to seal victory in a game during which several explosions were heard in the first half and the crowd briefly panicked at the end.
Police helicopters circled the stadium at the final whistle after Hollande had left for the interior ministry.
"We are all in shock," said Germany coach Joachim Loew. "The game and the goals move into the background on a day like this.
"We were told in the changing rooms what had happened. All of us on the bench were a bit scared because of a bomb threat earlier today when we spent three hours outside (our hotel)."
Germany were looking to restore some footballing pride with their FA locked in a 2006 World Cup scandal.
Forward Mario Gomez, making his comeback after an absence of more than 14 months and having missed the 2014 World Cup through injury, had a good first- half chance but was kept quiet after the break.
Giroud, on a hot scoring run having also hit six goals in the Premier League with Arsenal, might have netted a second for France when a diving header early in the second half sailed wide.
(Reporting by Karolos Grohmann, editing by Alan Baldwin)
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