My brother is considering to adopt his spouse's 2 minor children, she had them before. It would be a simple adoption. Our elderly mother is a widow. In the event that my brother dies before our mother, will the adopted children inherit her?

Yes, but…In the context of a simple adoption, the adopted child inherits from his family of origin and also from his adoptive family (Articles 364 and 368 of the Civil Code).
If your brother were to predecease your mother, his adopted children would represent their father in his mother's estate and therefore inherit from their (adoptive) grandmother.
However, children adopted in a simple way are not compulsory heirs with regard to their adoptive grandparents (paragraph 2 of article 368 of the Civil Code), your mother can plan to disinherit them by will.