The course at the Paris Institute of Political Studies - often referred to simply as Sciences Po - began on Monday, with twenty migrants taking part.
The students are aged between 20 and 40 years and are originally from Syria, Afghanistan and Sudan, with most already holding university qualifications from their own countries.
The aim is to help the migrants integrate in French society, but rather than just offering French classes, the university has decided to give the group of migrants the choice between French or English.
A spokeswoman for the university told The Local: "Most of the students we took on speak English so English language courses were offered because it was important to consolidate their level in this language.
"Secondly if they master English they will have a wider choice of courses to follow at Sciences Po, because many of them are taught only in English."
As well as joining the language courses, the migrants can also benefit from access to the university’s teaching resources, including the libraries and online materials, as well as extra-curricular activities such as sports clubs, societies and student events.
The scheme is set to last until June but if it is judged successful it could be repeated in 2017.
Language barriers are often cited as an obstacle to integration and employment for migrants and refugees arriving in Europe.
In France, there are no official language classes for new migrants run by the French state, but several charities and volunteer groups have offered French and English lessons in the country's refugee camps like the 'Jungle' near Calais.
However, if migrants are granted refugee status or asylum in France, they can enter into an "integration" contract with the state under which they receive free language classes for one year.
Sciences Po is known for its intensive programmes and has been a breeding ground for French leaders, with current president François Hollande and ex-president François Mitterand among its alumni.
Former President Nicolas Sarkozy also unrolled at Sciences Po, but he failed to graduate because his level of English wasn't deemed good enough.