Police moved in at dawn to remove the migrants, mainly from Sudan, Eritrea and Afghanistan, who were sleeping in tents and on mattresses in the camp in northern Paris.
Housing Minister Emmanuelle Cosse, who was present at the operation, said 2,083 people were evacuated to around 60 shelters in the Paris area.
The camp was already cleared of some 700 people a month ago.
France has received only a tiny proportion of the million-plus migrants who have crossed into Europe in the last 18 months, with many refugees seeing it mainly as a transit country to other destinations.
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Paris Mayor Anne Hidalgo announced last week that the city would open its first refugee camp in mid-October in a bid to take thousands off the streets.
Today's operation was the second major camp evacuation in the Paris area since July 22 when 2,500 people were taken to shelters.
Nearly 30 such evacuations involving some 19,000 people have been carried out since June 2015.
Many of those who land in Paris are bound for the port of Calais on the Channel coast, where they hope to stow away on trucks crossing to Britain.
According to a leaked interior ministry document, the government believes some 12,000 places are needed by the end of the year, much more than previously thought.
The insalubrious Jungle camp is home to at least 7,000 migrants. Charities say the number might be as high as 10,000 after an influx this summer.
Interior Minister Bernard Cazeneuve has vowed to close the camp "as quickly as possible" but said it would be done in stages.