The objective of Rainbow is to be compliant to the new GDPR (General Data Protection Regulation). GDPR will be applicable starting May, 2018.
Today, the Rainbow Essential offer is compliant with French Data Privacy law (Article 2 de la Loi Informatique et Libertés). The Essential offer is free of charge, targets anyone, and data is stored in France.
This is very clearly mentioned in Terms of Service that all Rainbow users agree upon subscription
The Rainbow services have been registered with the CNIL (French government body in charge of data privacy topics)
Compliance with any others country's regulation(s) must be determined with regards to French law and requirements.