Note: precisely, this June's election is the National Assembly ("Assemblee Nationale"), the lower house of France's bicameral Parliament. Partial elections for the upper chamber, the Senate, will be held in September.
Current and urgent affairs
As Bernard Masse has suggested in the comments, it is to carry current and urgent affairs ("les affaires courantes").
Note that the current legislative session is over until the next election, so the country, at least when it concerns legislative matters, is working at reduced speed.
Though new laws cannot be voted, the President and the government still have powers and duties. As a few examples (you can find more here):
- Preparation of laws: as leaders of their respective administration, Minister prepare and propose laws (ultimately accepted or not by the Parliament). Macron plans to changing laws about work very quickly, during the summer, so texts of law need to be prepared right now with the administration.
- Managing the budget.
- Nomination: the President and Ministers can nominate key members of the administration, with few control from the Parliament (as far as I know). These people can have a lot of power and influence, and can greatly interfere with a Minister's policy.
- Public order: the Minister of Justice and the Minister of Interior (Police) are in charge of public order. Police and justice have limited means, so they have to arbitrate about what kind of crimes should be investigated and punished in priority.
- Current affairs: similarly, Ministers are in charge to give directions to their administrations. For example, the Minster of Education has to prepare next school year, etc.
- War: as the chief of armies, the President has the power to decide to go to war. If memory serves, he can do so without Parliament's approval for 3 months.
Symbols are also important. The French President has quite of lot of powers and his personality is often considered as a factor of his election. For example, experts considered that former President Hollande was elected because he has a softer, quieter personality than his overactive predecessor Sarkozy.
Many people vote for a President hoping he will "change France". What a newly elected President do? Sit down and wait? That would give a very bad impression.
This is especially true in Macron's case as he built his popularity on his youth, his dynamism, and the promise he will renew political habits in France. His party was named "En Marche" (Let's go) before the elections, and now "La Republique en marche" (The Republic in Motion).
What is Macron's first government currently doing?
This article intitled "Philippe government: Projects on the menu of the first "real" week of work" (the government is called Philippe I, from the name of the Prime Minister Edouard Philippe. It will be followed by Philippe II if La Republique en Marche wins the elections and Edouard Philippe keeps his position). In short, the Ministers nominated their staff, and the government started working on several projects that were at the heart of Macron's political campaign, namely the reform of the Labor Code and the modernization of political ethics.