From the transcript:
Adam Shatz: ... something that is central to Barthes’s thinking, which is this discomfort with meaning. He described meaning at some point, I think, as sticky. Heavy, sticky. He didn’t like it. What was that about?Michael Wood: He says at one point – it’s a phrase I’ve always liked – I’ve always wanted to be exempt from meaning the way one is exempt from military service. It’s required – you can’t actually get out of military service if that’s the law of your country. You could be some kind of protester, you could be a conscientious objector, but he doesn’t want to be a conscientious objector. He wants a certain kind of exemption from meaning, or at least a rest from meaning. I think that is, in a way, a kind of French illness or a French worry. It’s a natural thing to say, I think if you’re French, that meaning is rather regimented, it’s official, there’s a standard version of it. I’m not sure that any English speaker ever quite feels that about meaning.
I think this is from "Roland Barthes by Roland Barthes," judging by the only other reference a quick search turned up: a 1977 review by Frank Kermode in the New York Times. Here's the excertp:
Barthes is an extraordinary virtuoso though people who read him in English—a language, incidentally, in which he takes very little interest—may be skeptical about this remark. It remains true. Highly original, extremely fertile and inventive, he really does represent, in a peculiarly qualified way, a new kind of writing, and he continually discovers new ways of writing about writing. He is not a philosopher, not a linguist not a poet, not a novelist and even not an essayist. His ideal “text” is not controlled by an author at all. He “dreams of a world which would be exempt from meaning (as one is from military service),” and the ideal text would also be without meaning and without style. Yet he is, and knows he is, a conscious stylist and heavy with meanings.
According to the biography in Roland Barthes by Roland Barthes, translated by Richard Howard, Barthes was indeed exempted from military service in 1937 (aged 22). I couldn't confirm the quote using the Amazon "Look inside" function, but the phrase "dreams of a world which would be exempt from meaning" apparently occurs on page 87 of the 2010 paperback edition.