"We'll be able to arrive at something as quickly as the political leadership in both countries want it to happen," Ms Charette said in a television interview. "Trade agreements will be easy to reach."
Britain is preparing to start talks to leave the 28-member EU just as the bloc finalises a trade deal with Canada after seven years of negotiations.
British Prime Minister Theresa May has signalled she wants to quit the EU so Britain can make trade deals with the rest of the world.
Ms Charette said that while Britain is still an EU member, it will benefit from tariff reductions enshrined in the new trade deal, which is known as the Comprehensive Economic and Trade Agreement.
The pact is to end 98 per cent of tariffs on goods from the outset and 99 per cent after seven years. After Brexit, the CETA agreement should serve as a model for the new UK-Canada deal, she said.
"There already is a trade deal, so the question is how do we revise it to make sure that the preferential access for investors and companies stays in place," she said.