Britain is to withdraw from a 50-year-old agreement allowing vessels from five European countries -- Belgium, France, Germany, Ireland and the Netherlands -- to fish within an area that is six miles (10 kilometres) off the UK's coast.
"We have to defend access to waters for artisanal and coastal fishing... without that there won't be any fishing," French fishing minister Stephane Travert told journalists after meeting his EU colleagues in Brussels.
The minister said that they had to "reach agreements" with Britain for when it leaves the European Union, which is expected in March 2019.
Britain on June 3 triggered a two-year withdrawal period from the agreement, the London Fisheries Convention, to meet a key Brexit pledge.
The agreement is in force alongside the EU's Common Fisheries Policy -- allowing vessels from EU member states to fish between 12 and 200 nautical miles off the UK -- which Britain will be excluded from after its exit from the bloc.
Travert said he wanted to "keep good relations" with London and to "do what we can so that everyone comes out on top from this situation."
He said closing Britain's access to the EU single market in this field was not necessarily the best solution "because that also takes the risk of closing markets for our processed food producers, many of whom work with the UK.
"So, we have to find space for discussions and space for compromise."
However the British government -- in political crisis after Prime Minister Theresa May lost her overall majority -- "themselves don't know if they are going for a hard or soft Brexit", the Frenchman added.
"We still have time, today we are only at the start of the process. We need to use what time we have to work together to find ways of reaching deals which will allow our French fishermen to continue to have access" to British waters.
British and EU negotiators separately began a second full round of Brexit talks in Brussels on Monday.
At the EU's insistence, Britain must first agree on the technicalities of its withdrawal before the Europeans will discuss a future trade deal.