France gradually lifted lockdown restrictions in May and June as the number of cases and deaths fell. The epidemic has killed nearly 30,000 people in France.
Castex, a low-profile former civil servant appointed by Emmanuel Macron, the President, last week, faces the daunting task of masterminding France's recovery from its worst health and economic crisis since World War II.
The crisis has wiped out the benefits of job creation attributed to Macron's business-friendly economic reforms over the past three years.
Thousands of jobs are being cut by Airbus, the aircraft manufacturer, the carmaker Renault and other large companies, and the economy is expected to shrink by 9 per cent this year.
The Government has pledged billions of euros in investments and measures to limit job losses.
However, data published yesterday by the national statistics office indicated that the French economy is set to rebound sharply in the second half of the year.
The data suggest there is a chance that France could return to pre-coronavirus growth levels by December.
The epidemic halted Macron's fiercely contested reforms of France's generous but convoluted pension system, which triggered months of protests.
Castex said his Government would reopen talks about the plans with unions and employers within two weeks.
Castex, who as a civil servant oversaw France's phased exit from lockdown, said: "We are going to protect people [from Covid-19], but above all we are going to invest in the transition to a more environmentally friendly economy, [and] in our country's recovery."
He added: "My aim is to prepare France for a possible second wave while preserving our daily life, our economic and social life."