I cant talk for France. But in Denmark the girls - called Tyskertøser(german girls/sluts) or feltmadrasser (military madrases ) - also had their heads shaved, some where attacked on the street and all the clothes rip of, they got burned/branded. Like this picture. (maybe NSFW, not nice anyway) http://www.b.dk/kommentarer/staten-gjorde-min-mor-til-tyskertoes

If the girls could get away with it they would move to another city and hide who the father was. The man in the article I linked is a son of a german soldier, and he never knew. But Denmark is small and it was not easy to hide it. Mainly because the Danish press actually printed names and personal information and called the children whore-children. It is estimated that around 10.000 - 12.000 children had German fathers. Some where taken from their mothers and adopted to others.

Just after the war there was a survey done in Denmark. 1% wanted the girls killed for treason. 5% wanted them in jail most wanted them to wear some kind of brand/mark like the Jews had been forced to. There was a general idea that the girls where prostituted, stupid and power hungry.

Not really something to be proud of. Like many things that happened just after war. Those who had been helping the Germans, or been making money on the war was in some cases shot on the street.

Women who had this done didn't necessarily have a child with a German soldier. They might have been a German's girlfriend.

As for the children: Keep in mind that it could be difficult during this time period to raise an illegitimate child so even leaving aside the issue of the father being a German soldier, such a women would have faced hardships and may have wanted to give their child up to be raised by others, anyway. But Germany actually had a program to seize and raise the children of Germans--it was called the Lebensborn program. It was designed to increase the number of Aryan children by encouraging births of German children, kidnapping Aryan-looking non-German children away from their parents, and kidnapping or accepting children fathered by a German soldier and a non-German mother and giving them to Aryan parents to adopt. As part of the Lebensborn program, they forcibly kidnapped many Polish children with no German parents, because the children looked Aryan and therefore were not to be raised by the "inferior" slavs.

The way children were treated after the war depended on the country. In Norway, such children were often mistreated badly. One of the most famous of these children is Anni-Frid Lyngstad, a member of the musical group ABBA.