The fishermen say they plan to continue blocking the northern French ports indefinitely.
The European Union sets annual quotas in an effort to protect and revive dwindling fish stocks.
Member nations negotiate each country's share of the total catch.
Jacky Henin, a former mayor of Calais and a European parliament member, said: "The immediate opening of supplementary catch quotas, for sole and cod, is vital for the future of small fishermen."
The French government said it may consider providing financial support to the fishing industry, but called the quotas reasonable.
Speaking to France 2 Television, Luc Chatel, a government spokesman, said: "France has not let fishermen down. If there are quotas, it is also in order to ... guarantee the catch for future years."
Chatel said France had increased catch quotas for certain fish in 2008.
Fishing industry representatives were set to meet in Paris on Wednesday evening with a senior official from the agriculture ministry.
Michelle Ulyatt, a spokeswoman for P&O Ferries, which normally runs 64 freight and passenger trips daily between the Calais port and Dover in England, said: "At the moment, we're putting as much pressure as we can on the French authorities."
Ulyatt said the company has considered bringing a suit against the French government in order to seek damages.
A poll published by BVA, a French market research company, on Wednesday appeared to suggest protesting French workers have public opinion on their side.
The results showed 55 per cent of respondents consider "radical social actions" by workers are justified. Sixty-four per cent said such actions should not be punished.
The poll was conducted by telephone on Friday and Saturday among 1,014 people nationwide. No margin of error was given.