All adults who leave France will receive about $380 and all children $100.
Those who have not agreed to voluntarily return will face forced removal without any cash benefit in a month's time if they do not comply with the regulations for staying in the country.
Nicolas Sarkozy, the French president, has ordered the controversial crackdown on the Roma, traditionally a travelling people.
The case has raised significant concern over discrimination within Europe and calls for Roma communities to be satisfactorily integrated.
Teodor Basconschi, the Romanian foreign minister, warned against "xenophobic reactions" after the economic recession in Europe.
"What has happened in Paris shows that we must have an integration plan across Europe for Roma citizens," Basescu told reporters.
Besson reacted against criticism of France, stating in an interview with France 2 television: "France is the country in Europe which most respects the rights of foreigners, notably foreigners in irregular situations."
"Or - let's be more modest - one of the most respectful countries, so we do not have any lessons to learn.
"Last year, we gave out 170,000 long-term residency permits. We have become the second country in the world after the United States in granting asylum."
The EU has said that the bloc's freedom of movement laws must be adhered to by France when expelling Roma deemed to be living illegally in the country.
France has said that this is the case.
About 15,000 Roma reside in France, being of Eastern European origin.
Romanian official statistics state that 530,000 Roma live in their country. However, some non-governmental organisations have said that the actual figure is as many as 2.5 million, but that many Roma do not declare their background due to fears of discrimination.