Non European students holding a French student residence permit must remember that their French residence permit is valid for France only, allowing them to reside temporarily in France to study.

This French permit allows them to circulate within the Schengen area, not reside, especially to do an internship or an exchange program.

For example : 

Li is a Chinese national, holding a French student residence permit. Li has relatives in Germany and in Spain. He can go and visit his relatives during the winter holidays as long as his French permit is valid. Li may evidently return to France but to play it safe, Li enquired with the German and Spanish consulate in Paris to verify if he could enter Germany and Spain as a tourist with his French student residence permit. Double checking is the key word when national laws can change rapidly.

Ashok is an Indian national, also holding a French residence permit. Ashok should go to Sweden to do a 6-month internship. Since his French residence permit is valid during the whole duration of his internship, Ashok leaves for Sweden without carrying out any other formality. Two weeks later, the company asks for his Swedish work permit. Not being able to provide any such document, Ashok must immediately leave Sweden. 

Mario is a Brazilian national, also holding a French residence permit. Mario has been assigned to the USA for a study abroad semester. Mario has started applying for his US visa but the American consulate sees that his French student residence permit is due to expire within the next two months. Because Mario cannot prove that he'll be authorized to re-enter France once his exchange program in the USA will have ended, Mario will most likely be denied his US visa.

Conclusion : ESSEC students must plan ahead. 

They must verify the validity of their French student residence permit, do the needful in case the French permit is due to expire shortly or while they are outside France. 

They must enquire at the consulate in Paris of the destination country they intend to go to, explain clearly the purpose of their visit, justify their revenues, apply for a visa or a work permit if need be. Depending on student's nationality, laws of the destination country will vary.

As a French school, ESSEC may not whatsoever intervene in a foreign country's national laws. It is already ESSEC's first obligation to be in compliance with the French laws.