Of the countries that you list here, only Italy fits the description given in the question. Italy most definitely has a major divide between its north and its south.
Of the other countries you mention, Spain and Greece both have serious economic problems. However, their problems are not primarily regional. France is a relatively strong economic country. By contrast, Italy is a country that can seem like two different countries. The North is economically quite prosperous. It is seen as a region that is more similar to places like Germany than to Southern Italy. The South is rather backwards. The problem is so great that there is a good deal of tension. Northern Italians sometimes refer to Southern Italians in racist ways, essentially comparing them to Africans since they are relatively near to Africa.
Thus, the country that is divided in the way this question suggests is Italy.
The answer given above (Italy) does indeed best fit the description of a country divided between its prosperous north and its economically-depressed south. Italy, despite its ancient history, has only been a unified nation since 1861. It was then that its disparate city-states were formally merged into the nation we know as Italy. Of the four options provided in the student's question -- France, Italy, Greece, and Spain -- Italy does qualify as the country that has a progressive north and a stagnant, economically-depressive south.
It is interesting to note, however, that a great political issue for Spain has been its division into two major regions, Spain and Catalonia, the latter being a major province that continues to agitate for independence from Spain. Catalonian (or Catalan) independence movements, including the terrorist organization ETA (the Spanish initials for the Basque Homeland and Liberty) are strong and resilient and continue to push for independence, both diplomatically and violently.
While Italy is divided between its prosperous north and its economically depressive south (making it the correct answer choice here) it is important to recognize that Spain's divisions are also very real and arguably pose a greater threat to national unity than does the north-south division that characterizes Italy.