Stena says its new Dublin to Cherbourg service sold out on its first day, with 175 trucks booked to sail.
However, hauliers say direct routes to Europe cannot take the place of the British landbridge because of the lack of capacity and extra costs involved.
The Stena Estrid sailed from Dublin to Cherbourg, France at 3pm after being taken off the Holyhead route for the weekend.
Simon Palmer of Stena said they are responding to customer demand over fears of delays going through Britain.
He said traffic on the Holyhead route is down 50% and the company wants to test demand on a weekend Cherbourg route with the Estrid sailing out on Saturday and returning Sunday.
Mr Palmer says that Stena has also seen a 120% increase in freight traffic out of Rosslare.
He said there are difficulties with the direct Europe route as the Celtic Sea is part of the Atlantic and is more prone to cancellations because of bad conditions.
Although hauliers have welcomed the new route, Brendan Dixon of Dixon International Transport says there is still nowhere near enough capacity.
He says his company usually take 100 loads a week to Europe but at present they can only get bookings for 25 to 30.
Mr Dixon calculates that the French route doubles costs because of 19-hour sailing time and because Cherbourg is 700km away from his company's trucks' destination in Belgium, Holland and Germany.
Linda Stuart Trainor of Food Drink Ireland said the direct route is difficult for many of her organisation's members because Ireland is a small import market which has relied on distributed loads from Britain.
She has called on the Government to work out a solution to the threatened tariffs of between 8% and 30% for foods imported from British distribution centres.
The Revenue Commissioners said in a statement that they are meeting regularly with trade representatives to deal with concerns but it cannot set aside compliance with customs regulations.
The statement added: "This would carry with it serious consequences for the view taken by other member states of exports from Ireland and their automatic right to free circulation within the European Union. Such an approach would be highly detrimental to Irish trade and business and the Irish economy in general".