A 41-year-old French woman and her 55-year-old partner were brought before a judge in Setúbal on Friday following their arrest in Portugal.
The two French boys aged four and five were found crying by a roadside near Alcácer do Sal on Tuesday evening. They were placed in a foster family after a hospital check.
The mother, based in Colmar, and her partner were arrested on Thursday in Fátima. They were taken to the Setúbal court where they are to be heard by an investigating judge.
The children's father had reported their disappearance on May 11. French authorities issued a European arrest warrant. The couple faces charges of abuse, endangerment and abandonment.