The summons for Abdul Halim Khaddam, 73, sent through Interpol's Damascus office, requests that he be turned over to Syrian authorities on charges that include inciting a foreign country to attack Syria.
A top member of Syria's ruling elite for nearly 30 years, Khaddam provoked an outcry in December when he told an interviewer that Bashar al-Assad, the Syrian president, had threatened Rafiq al-Hariri months before the former Lebanese prime minister was assassinated.
Assad has denied the allegation.
On Sunday, Hossam al-Deen Habash, the attorney who filed the lawsuit against Khaddam, told The Associated Press that if Khaddam does not return, he will be tried in absentia.
The summons is unlikely to be respected as Khaddam and his family have lived in France since he retired as vice president last summer.
But Habash was hopeful that France would respond positively, saying that turning over Khaddam would show "its respect for international justice and its refusal to harbor wanted persons".
Syria denies involvement in the
blast that killed al-Hariri in 2005
The Interpol request follows two earlier summons issued by a Syrian court.
The most recent, published in the government newspaper Tishrin on May 7, said that Khaddam, his wife and 23 family members - including sons, daughters and their husbands, as well as grandchildren - must appear in court in the northern town of Banias on June 12.
Syrian state media promptly denounced Khaddam, and Syrian legislators called for him to be prosecuted for treason.
Attorney Hossam al-Deen Habash said he had filed a lawsuit against Khaddam for providing a foreign country with "pretexts" to invade Syria and for establishing contacts with Israel.
Syria denies any involvement in the massive truck bombing that killed Hariri and 20 other people on February 14, 2005, in Beirut.
But Hariri's assassination triggered a major shift in Lebanese politics, which - along with international pressure - led Syria to withdraw its troops from Lebanon last year and ending nearly three-decades of domination of its smaller neighbor.
A Syrian military court charged Khaddam last month with plotting to take power and, in an apparent reference to the US, inciting a foreign attack against Syria.
Syrian authorities have seized real estate owned by Khaddam's son and registered in the names of some of his employees, the Tishrin newspaper reported on Sunday.