President is elected, assembly is elected, president picks a prime minister among the majority party in the assembly (hopefully the same as his own, since the assembly gets to confirm the pick), prime minister picks a government (picks the ministers in their own party) with the president’s blessings. In case the majority party is opposite the president, the president doesn’t get much of a choice, as we know the majority party will only accept ministers on their side.
When the assembly is reelected, the prime minister typically offers their resignation regardless of the results (we are here), and the president can accept it or refuse it (we expect Macron to refuse, or at least delay it until the end of the Olympics, which makes the most sense, but Attal will almost certainly be gone after the Olympics). Then a new government is formed. A prime minister usually gets a couple governments under their belt until the president gets a new prime minister. Attal got shafted by the early dissolution since he was only here for a few months.