Month-long strikes over pay and the cost of living had escalated into violence in Guadeloupe.
Hundreds of police reinforcements were deployed from mainland France after a labour activist was shot dead late on Tuesday near a barricade in Pointe-a-Pitre.
Strikers are demanding a raise of $250 a month for low-wage workers who now make about $1,130 a month.
Nathalie Minatchy, a Labour movement organiser in Gaudeloupe, told Al Jazeera the French president's offer was not good enough and that the strike would continue.
"The strike will not stop now. The government pledge is not enough for the strikers," she said.
"We must continue until we get what we want."
| There is rising discontent over the high levels of unemployment on the island [Reuters]
Our correspondent said that residents of the island were looking for fundamental economic policy changes to be made rather than simple aid.
"People say its not a cash handout they are looking for. What they want is some kind of real change in the way this island is run.
"This island gets about half a million tourists a year but there are a lot of people living in poverty," he said.
Sarkozy said he understood the frustrations of the island's residents, which suffers from an unemployment rate of more than 20 per cent - almost three times the level in mainland France.
"I know the frustrations, the injuries, the suffering that have to be overcome," he said on RFO, the public radio network that serves France's overseas regions.
Sarkozy also said he would travel to Guadeloupe as soon as calm returned.
With a population of about 450,000 and an area of 1,700sq km, Guadeloupe is heavily dependent on expensive imports for fuel and food.