The US VP analogy is possible but potentially confusing since for it to be more accurate you'd have to imagine the VP as representing the senate majority (actually it would have to be the congressional majority) not necessarily the president's party or choice. France had many years of "cohabitation" governments in which the president was from the right or left and the PM was from the opposite party which was the ruling majority in parliament. Presidential terms in France were for 7 years up until 2001 when they were reduced to 5 years. This was plenty of time for the electorate to decide they had had enough and change the parliamentary majority thus forcing a cohabitation government.

The brookings institute's web site has an article by Olivier Duhamel, Professor of Constitutional Law and Political Science at Sciences Po Paris, that discusses the French electoral system and provides this graph of the 5th republic presidents and prime ministers illustrating the cohabitation of red and blue: