The transcript of the meeting was published on Monday, hours before he arrived in London for the latest round of post-Brexit trade discussions with David Frost.
But Simon Collins, executive officer of the Shetland Fishermen's Association, warned against viewing Mr Barnier's words as a generous offer.
He pointed out that under international law the UK is no longer bound to the CFP.
Mr Collins told Express.co.uk: "Barnier is playing a bit to the gallery there.
"It's a bit like saying he'll allow the sun to come up - which is very generous of him because it's no longer in his gift actually.
"He's offering a concession over something which he actually has no power over because the default position in international law is once we left the EU, which we did legally at the end of January, we then have all the rights and responsibilities of an independent coastal state.
"So we are actually in charge of our waters - that's the default legal position.
"So what Barnier is doing is he's giving his gracious permission to be where we already are legally. Express.
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