Securing Ingrid Betancourt's release has become a priority for Mr Sarkozy
French President Nicolas Sarkozy would travel to Colombia's border with Venezuela to free a French-Colombian hostage, his foreign minister has said.
Bernard Kouchner said France was still waiting for a direct response from Farc rebels about a mission to aid Ingrid Betancourt, who is seriously ill.
A senior Farc leader had suggested earlier Farc had not agreed to grant access to the high-profile hostage.
He said Farc would only release hostages through a prisoner exchange.
"If there were a hope, (Venezuelan President Hugo) Chavez and Mr Sarkozy would go to get Madame Betancourt at the frontier," said Mr Kouchner.
'We're in place'
But Mr Chavez, who has helped broker the release of six Farc hostages this year, warned he could not help without guarantees from the US and Colombia.
"We are willing to continue helping, but a series of gestures are needed from the Colombian and US governments (to establish) a minimum of trust that allows us to reactivate the paths toward a release," he said.
Lorenzo Delloye, Ms Betancourt's son, said earlier this week she had Hepatitis B and urgently needed a blood transfusion to stay alive.
The French mission was sent to Colombia on Thursday after the government promised to suspend military operations against Farc in the area where many of its hostages are believed to be held.
But on Friday the medical team remain grounded at a Bogota air base.
"We're waiting, we're in place," Mr Kouchner told Europe 1 Radio on Friday.
"We're trying, trying, trying and there's no other solution."
In a statement posted on the ABP news agency's website, senior Farc rebel Rodrigo Granda suggested he had neither agreed to grant the French mission access to Ms Betancourt nor to release any hostages unilaterally.
The French humanitarian mission landed in Colombia on Thursday
"Only as a result of a prisoner exchange will those who are held captive in our camps go free," he said.
He added that the group could not be asked for "more peace gestures", as it had already displayed enough political good will by releasing six political hostages earlier this year.
Colombian President Alvaro Uribe has promised to make "all possible efforts" to help free Ms Betancourt, and his country's military chief, Gen Freddy Padilla, has offered to facilitate the French mission.
Gen Padilla said the French team, which includes two doctors and two diplomats, did not know where she was being held, although French officials in Bogota and Paris have refused to confirm this.
Mr Kouchner had initially voiced high optimism after the military plane carrying the French mission had landed at Bogota's Catam air base.
Born on 25 December 1961
Grows up in Paris
1989: Returns to Colombia
1994: Elected to lower house
1998: Becomes a senator
2002: Kidnapped by Farc rebels
"We have done all we humanly could and now we need to wait for our envoys, the doctor, to reach the field," he said.
Last week, France offered to take in rebels released from prison in exchange for the 46-year-old, who has been held in the jungle since 2002.
Ms Betancourt - a former Colombian presidential candidate - was pictured looking thin and frail in a recent video.
She is one of 39 high-profile hostages whom Farc would like to exchange for 500 rebels currently in prison.
The rebel group has been fighting the Colombian government for over 40 years.