Macron is the president and head of state. He’s elected directly by the citizens of France.
Attal is (was) the prime minister and head of government. He’s elected by the members of parliament. He’s appointed by the president but needs majority support in parliament.
“To form a government” usually means that someone is tasked by the head of state (president or king) to come up with a group of people (cabinet) that has majority support in the house(s) of parliament. That’s easy for Starmer when Labour has a majority. In other countries like the Netherlands, Germany, or Italy, that usually requires a coalition.