The French Commissariat Général à l'Egalité des Territoires (CGET) has just published a study with a whole section on cross-border labour mobility.

It underlines that cross-border labour mobility is increasing in the EU and can sometimes represent up to 40% of the people who are working in a given territory. This happens despite several obstacles: languages, access to information on vacancies, differences in the labour law (pension, social security, etc.) as well as recognition of diplomas and qualifications. The study also makes a typology of the different borders in the EU and presents interesting maps on the situation along the French borders. 

It is the Chapter 6 in this document:

http://www.observatoire-des-territoires.gouv.fr/observatoire-des-territoires/sites/default/files/images/Rapport_ot_2017%20-%20moy_def.pdf