The reigning world and European champions took the lead in the 25th minute when Sergio Ramos converted at the second attempt. The Real Madrid defender's first effort came back off the post, but he reacted quickly enough to turn the rebound in.
Just a minute later Spain were handed a golden chance to double their lead as Laurent Koscielny brought down Pedro in the box. Cesc Fabregas stepped up to take the spot kick, but Hugo Lloris guessed correctly and palmed his effort away.
Lloris kept his side in the match again on the stroke of half-time with a fine double save, first from Pedro and then from Fabregas.
Spain were punished for their failure to grab a second when Giroud headed in Franck Ribery's cross in the fourth minute of second-half stoppage time to give his side a point.