International Covid-19 news: Nearly 396,000 deaths, France reboots tourism
Castex was named by President Emmanuel Macron last week to lead a new government tasked with orchestrating the country's recovery from its worst health and economic crisis since World War II.
Billions of euros have been promised for investments as well as measures to limit job losses in an economy expected to shrink around 10 percent this year.
"We are going to protect people, but above all we are going to invest in the ecological transformation, in our country's recovery," Castex said.
He also confirmed he had increased a proposed wage hike and budget boosts for hospital staff by around one billion euros in negotiations with unions this week, bring the total envelope to 7.5 billion euros ($8.5 million).
But union leaders say that would lift monthly pay for nurses, technicians and others on the frontlines of the coronavirus fight by only 180 euros a month, far short of demands for a 300 euro raise.
The outbreak has killed nearly 30 000 people in France since the first cases were reported in January.