Mr Vedrine hopes to promote peace in DR Congo
Mr Vedrine is on the third stop on a four-nation tour of the Great Lakes region of central Africa.
Earlier he held talks in the Rwandan capital, Kigali, with President Paul Kagame.
The BBC correspondent in Kigali says Mr Vedrine acknowledged Rwanda's concerns over its border security and urged neighbouring countries and other protagonists in the Lusaka peace accord to help resolve the problem.
It was the first time since 1978 that a French foreign minister had made an official visit to Rwanda.
Mr Vedrine's visit was also billed as an attempt to normalise bilateral relations with Rwanda after the 1994 genocide.
France gave critical backing to the former Rwandan regime of the late Juvenal Habyarimana, whose assassination sparked the genocide, before and during the bloodbath.
France has been accused of helping those suspected of atrocities to escape the country under an initiative - ostensibly humanitarian - known as Operation Turquoise.
At least 800,000 people are estimated to have been killed in the space of 100 days in 1994.
Most of the dead were Tutsis and those who perpetrated the violence, mainly Hutu.
Congo tensions
Before Kigali, Mr Vedrine paid a brief visit to Uganda where he met President Yoweri Museveni and the Congolese rebel leader, Jean-Pierre Bemba, whose armed insurgency in neighbouring Democratic Republic of Congo is backed by Uganda.
Mr Vedrine is also due to visit Kinshasa for talks with the DR Congo President, Joseph Kabila.
President Kagame, in a newspaper interview earlier this year, said he had not seen any significant change in France's relations with Rwanda, although the Rwandan embassy in Paris is due to reopen next year.
The Democratic Republic of Congo is another point of contention in Franco-Rwandan relations. France has been active within the United Nations at Security Council level in putting pressure on Rwanda to pull out of DR Congo completely.
The Rwandan Government thinks that France, along with the former colonial power, Belgium, is far too keen to give legitimacy to DR Congo's President Joseph Kabila.
Disarming Hutus
Meanwhile on Monday, the British Government announced it would finance a scheme aimed at disarming Hutu rebels blamed for the genocide.
The announcement was made by the British international development secretary, Clare Short, after she concluded a tour of the region.
The scheme, costing $7m, will target Hutu militias in the DR Congo.
Ms Short said the money would go to women who could persuade their men to give up their weapons and return home.
She said disarming Hutu fighters would also reduce concerns by Rwanda and Uganda over their own security, encouraging them to end their involvement in the fighting in the DR Congo.