Vernet stressed that the police officers were in no way responsible for Bino's death.
Nicolas Sarkozy, the French president, said he would meet with elected officials from the island on Thursday, to "address the anxiety, worries and also a certain form of despair from our compatriots".
Sebastian Walker, Al Jazeera's correspondent in Pointe-a-Pitre, said: "The protesters say they have been ignored by the French government for many years.
"Unemployment here is the third highest in the European Union. Away from the luxury hotels and resorts there is a severe economic situation that has angered a lot of people."
Union leaders have said that the situation in Guadeloupe is spiralling out of control, and there are fears that the unrest could spread to mainland France.
Bino is the first victim of the violence on the island which has been crippled by strikes that began on January 20 over low pay and the high price of basic goods.
Earlier in the week, protesters set buildings and cars on fire, looted shops, smashed storefront windows and clashed with police in Point-a-Pitre and at least two other towns.
Thousands of tourists have also fled the island and neighbouring Martinique.
Strikers' are demanding a raise of $250 a month for low-wage workers who now make about $1,130 a month.
On Thursday, Francois Fillon, the French prime minister, said the government would make a new wage offer to strikers.
"Mediators have come up with a proposal which I am going to assess and which will be submitted to employers and the unions," he told French radio RTL.
"This allows us to get very close to the quantified financial goals of the workers."
Underlying much of the unrest in Guadeloupe and Martinique is anger within the local Afro-Caribbean community - many of whom are descendants of slaves brought to the island by France - that the vast majority of wealth and land remain in the hands of colonist descendants.