To apply for the new France Residency Card online, you need to go to the following French government site https://contacts-demarches.interieur.gouv.fr/brexit/brexit-demande-titre-sejour/, before you apply you will need to prepare the documents that are needed to accompany the application (each document file must have a different name and be less than 5mb in total).
Further information can be found on the French Government Site in English spread over 3 pages: https://mobile.interieur.gouv.fr/Actualites/Le-ministere-de-l-Interieur-se-prepare-au-Brexit/Sejour#113660_children
A flow chart of the documents needed (in English) is available here…

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