Be clear about the contract and the host organisation or employer (there won’t be any support for a summer job or employment) or the hosting conditions with a family. Check the terms and conditions for internships in your learning agreement with the institution or employer.
Registering at the consulate or embassy is recommended and in some cases mandatory.
Look into whether there is a French consulate in the destination country, especially if you are not going to the capital. It is a good idea to register just in case you need to use the consular services sometime in the future.
Lastly, check your private insurance against the coverage included in the contract or the programme to make sure you are fully covered.