The French, who have now gone 18 games undefeated after losing the first two under coach Laurent Blanc, grabbed the lead after 21 minutes when Giroud slotted in through goalkeeper Tim Wiese's legs.
Substitute Malouda fired in from close range midway through the second half before Germany substitute Cacau cut the deficit in stoppage-time.
"We knew that Germany were very strong offensively but we had studied a few weaknesses in the defence," Blanc told reporters.
"I fully enjoyed this game because it was two countries playing attacking football and of course my pleasure was ten-fold because we won," he said. "We had good chances, we saw goals and that was great."
The visitors, sprightlier than the hosts from the start, had the first real chance with Yohan Cabaye's header cleared on the line by Wiese in the 16th minute.
Real Madrid's Mesut Ozil, back at the Weser Stadium for the first time since leaving Werder Bremen to join the Spanish club in 2010, tried his luck from 25 metres with his shot flying narrowly wide on the stroke of half-time.
"We are obviously a bit annoyed with the result but I am more annoyed about the way we lost," Germany coach Joachim Low told reporters. "We did have some chances in the first half but France were better."
"We had too big gaps in the defence. But we must keep in mind it was a long break since November, there were some changes, some injuries and you can lose your rhythm a bit.
"Once we are together for three or four weeks it will be much better."
