Who are among those who Chirac may name as premier?

Le Pen knocked Jospin out of the French presidential race. If Chirac, as it seems, will fly home free on May 5, who will he choose as premier? What will determine who he chooses? Will there be new Assembly with a new coalition of forces? Is there a new election for the Assembly coming up, from whose leaders Chirac will choose?

IIRC, the president appoints whoever can put together a ruling bloc in parliament - so he might have to appoint a socialist, as he did when Juppe handed over to Jospin - even though he’s a conservative.

The parliamentary election is in June.

Weird system - either have a directly elected president with executive power or a parliamentary system. But both?

I am not french but I believe Hemlock is correct. Who becomes prime minister depends on the results of the election for parliament. The prime minister is normally the leader of the biggest party (or the party that can put together a coalition with a majority of the votes).

Thanks, Hemlock, and Coil. So the President waits until the legislative elections, and, as in other systems (British, Weimar), names as prime minister the one most likely to run a government, by means of patchwork coalitions with other parties, etc. What are the names of these possible premiers?