The report also shows that border police do not have the means to control the new arrivals .
The French government has responded by saying France is a transit country for migrants, many of whom travel to Calais hoping to reach Britain.
But as Christophe Harrison of the asylum seeker support group France Terre d'Asile told RFI, some of these Eritreans are also seeking refuge in France.
The influx of migrants to France looks set to continue, as he explains:
"Italy has been alerting European countries and the European Union about this rise of migrants crossing the sea but they received no appropriate answer. So in a way we can observe a mechanical phenomenon because if Italy is struggling alone to give these migrants access to effective asylum procedures or opportunities for integration, mechanically some of those migrants will continue their way to other countries, like France or the UK."
Authorities say the increase in migrants trying to cross into France is due to the rise in migrants crossing from Africa to Italy -- over 61-thousand so far this year , as opposed to about 8-thousand and 4-thousand for the same periods in the two previous years.