While the Germans did not officially annex Alsace-Lorraine (Elsass-Lothringen) into the German Reich (but did plan to do so when the war was concluded and German occupation of France ended), they did declare the people there German citizens and started conscripting them in October 1942. Most of the some 130 000 men conscripted this way served on the Eastern Front, most likely because the Germans did not trust them serving against the Western Allies, especially the Free French, fearing they would desert and join the enemy. Roughly 40 000 of the conscripts fled (mostly to Switzerland) or deserted to join the resistance or the Western Allies. This was at great risk, as the Germans arrested and deported the families of those that fled or deserted to concentration camps. The Soviets also send 1 500 men captured on the Eastern Front to Algeria in 1944, where they joined the Free French. The conscripts were known as malgré-nous (roughly translates as 'against our will').
A small number of the conscripts served with the 2. SS Panzer-Division 'Das Reich' and 14 of them (12 conscripts and 1 volunteer) took part in the massacre at Oradour-sur-Glane, for which they were sentenced to 5-11 years in prison (for the conscripts) and death (for the volunteer) after the war. However, after public outrage in Alsace, the conscripts were pardoned.
The view of the conscripts varied from unfortunate victims to national traitors.
The rest of occupied France, the northern part until Vichy France was dissolved in November 1942 and the whole of France after that was still formally under French jurisdiction and the people French citizens that were not subject to German conscription.
The Germans did raise a voluntary SS formation, the 33. Waffen-Grenadier-Division der SS 'Charlemagne' during 1944 from a motley collection of an earlier volunteer regiments and various collaborationist organisations raised during the German occupation of France. It never reached more than brigade strength and was like msot SS formations a second to third rate formation at best, more fit for war crimes and occupation duties than battle against reglar forces.