Having taken back the French presidency after 17 years in exile, the French Socialists must be regarded as heavy favorites to complete a political sweep in June when France votes in legislative elections.
The French 5th Republic may not have exactly worked out the way its architects Charles DeGaulle and Michelle Debre intended, but it is still essentially a presidential system.
Legislative elections that followed shortly after a presidential election, resulted in victory for the party of the president.
This occurred in 1981 and 1988, after Mitterrand won the presidential contests and in 2002, following the reelection of Jaques Chirac. If you have already elected a president, you give him a to go with that victory.
France shows much less of an inclination than the United States to split power between a president and a legislative majority. The French have done so in the past, but that was the time when presidential terms lasted for 7 years, whereas the National Assembly was voted in for a period of 5 years. Therefore, in 1986 1993 and 1997 you had the exceptional cases of the parliamentary victory going to the party that did not hold the presidency.
They were votes against the president before his term expired.
Although there is only one month till the legislative elections, the new president to already appoint a Socialist Prime Minister who will be the incumbent, even if it is is for only a month's time.
The second reason is that with Nicolas Sarkozy out-of-the-way it is not certain whom the center-right will decide upon as a person who will lead them into the legislative elections and if victorious would become the Prime Minister.
The most important reason to expect a Socialist victory is unity on the left versus division on the right. The left showed up at the second ballot united and the expectation is that the good feeling will continue through the legislative election. If President Hollande subsequently decides that he will not be able to fulfill most of his campaign promises, the defections and acrimony will begin. but for now the left is on a roll.
The opposite situation prevails on the right. Marine Le Pen, who effectively doomed Nicolas Sarkozy's chances by advocating a blank ballot, is set to play the same game in the legislative elections. As long as the center-right boycotts the National Front, the National Front will return the compliment, thus allowing candidates of the left to mop up the legislative districts.
If, as expected, the Socialists take the National Assembly, then the left will for the first time in the history of the 5th Republic control all the levers of power-- both houses of the legislative branch, and local, regional and central government.