The network believed to have brought hundreds of people from Iraq, Afghanistan, and elsewhere to Scandinavian countries, Britain and Ireland in recent years.
Paris prosecutors said in a statement that police had uncovered a "well-structured transnational cell" and arrested 24 people in the capital and other French towns and cities.
The French interior and immigration ministries said in a joint statement that at least 1,300 police officers from 10 European countries were mobilised for the probe.
The would-be immigrants paid between $9,300 and $21,000 to be brought to Europe, French and German authorities said.
In Belgium, police detained 10 people during raids in the capital, Brussels, and in nearby city of Leuven.
Some of those detained are believed to be ring leaders, Belgian police officials said.
Seven people were arrested in Germany.
Horst Hund, a German prosecutor spokesman, said the seven people were among 15 individuals that authorities have been investigating since the beginning
of the year.
In Sweden, 12 people were detained in connection with Operation Baghdad.
In the Netherlands, border police in the northern city of Leeuwarden arrested three men "suspected of involvement in a European network of human smugglers", the Dutch national prosecutor's office said.