Douste-Blazy announced his intention to stand for boss of the UN's health organisation in an interview with the Journal du Dimanche newspaper.
A vote on the position will take place in May 2017.
"We can't live in a world where two billion human beings do not have access to essential medicines and vaccins," he said.
There should be health equality for all humanity, he added and called for "the creation of universal health coverage so that everyone has access to health".
Douste-Blazy, a cardiologist by profession, has been head of Unitaid, a global health NGO largely financed by a levy on airline tickets and based at the WHO headquarters in Geneva, since 2006.
He was a member of the Centre for Social Democrats, which was part of former president Giscard d'Estaing's UDF, before joining the mainstream right UMP, now the Republicans.
Douste-Blazy was France's health minister in 1993-1995 and 2004-2005, culture minister in 1995-1997, foreign affairs minister in 2005-2007 and mayor of the south-western cities of Lourdes (1989-2000) and Toulouse (2001-2004).
Although his political career was on the right, he says that France's Socialist president has been campaigning for him "since we talked, about six months ago".
"This is the candidacy of a country not of a person, by the way," he told the paper. "France really is a force. All of us are capable of being above partisan differences when it's a matter of the country's interest."
France could soon lose the UN's most prestigious post after holding it for 20 years, according to the Mediapart website.
The US is campaiging to take the leadership of the department of peace-keeping operations away from France when the UN secretary-generalship changes hands at the end of the year, the site claims.
Washington is using the body's apparent attempts to hush up sex-abuse scandals in the Central African Republic to discredit the agency's current head, Hervé Ladsous, and end a 20-year understanding that a French national would hold the post, according to Mediapart.