The parliament is elected from the 577 “circonscriptions”, or small bit of continental and non continental France + French living abroad, as seen on this map. They represent all of France in front of the government, they vote for or against laws at a national level. They do not take care of any local politic.
Normally the parliament is elected every 5 years, a few weeks after the presidential election so the president can have a parliament on the same side as his.
But the among the president powers, he can dissolve the parliament, so those 577 deputies are sent home and a new election takes place. It is usually done to have the same political party everywhere so passing new laws is easy.
As the government (prime minister and ministers) generally comes from the most represented party in the parliament, if the majority shifts to another party then the prime minister have to resign (all his ministers are included) and a new government will be made from the new majority (in today’s case, the left, even if the president is central-right).
The president have to wait one year before dissolving the parliament again. So he could technically dissolve it again until the next presidential election in 2027.
So for today it means that the PM and his government have to resign (which is done). The president will then have to choose a new PM from the leading party at the parliament (left Front Populaire) and will have to work with a government not agreeing with him.
It is named a cohabitation, between a right side president and left side government, which by itself is not such a big deal as countries like Switzerland works like that, a perpetual compromise between various political views. But France (or US, or ???) is not used to that, so this could lead to a government achieving nothing cause every political side will vote laws according to their own views and nothing is accepted.