The operation targeted 2,500 migrants sleeping rough near Paris's Stalingrad metro station.
The first bus carrying migrants to refugee centers across France has left the Calais camp.
Xavier Bertrand's suggestion is supported by French presidential candidates.
The summer surge in 2015 overwhelmed immigration officers.
Emmanuel Macron said a Brexit could also result in an exodus of London's financial workers.
French authorities said they would offer 750 migrants spaces in a state-run shelter; others would be encouraged to move to other migrant centers.
Thirteen people have died attempting to cross the Channel since June.
About 200 migrants attempt to get to Britain via the tunnel from Calais.
The 65-mile Critical Mass to Calais ride sees a big show of solidarity.
The decision to prosecute 40-year-old Rahman Haroun has been criticized by migrants' rights groups.
Poor health conditions, makeshift churches and lessons in applying for asylum form aspects of life in The Jungle.
The Sudanese man was arrested by British police close to the Folkestone terminal in Kent.
The European Commission will transfer almost 50 million euros to tackle the growing crisis