Alitalia has been losing money for the last five years, and has been struggling to find a solution to its problems.
The proposal by Air France to buy Alitalia has a number of problems to be overcome before the deal is finalised and is expected to become an important subject in Italy's general election, which takes place on 13 and 14 April.
Air France are seeking backing for the move from the Italian trade unions.
The Italian government will have to sell its shares in Alitalia before the deal can go through, and Italy's stock market as well as the European Union competition regulators have to give their go ahead for it too.
