I think that Barthes' sentence "boxing is a Jansenist sport" may be more conspicuously rendered like this: the common form of boxing (unlike the common form of wrestling) is a genuine sport.
First, it is clear, within Barthes' The World of Wrestling, that by the word "wrestling" he did not mean the genuine sport, the Olympic (Greco- Roman) type of wrestling. Rather, he intended what is called professional wrestling, a make-believe wrestling match, a familiar type of circus-like show. Barthes even called the genuine sport "false wrestling".
Of course, there exists a false wrestling, in which the participants unnecessarily go to great lengths to make a show of a fair fight; this is of no interest . . . True wrestling, wrongly called amateur wrestling, is performed in second-rate halls, where the public spontaneously attunes itself to the spectacular nature of the contest, like the audience at a suburban cinema . . . The public is completely uninterested in knowing whether the contest is rigged or not, and rightly so; it abandons itself to the primary virtue of the spectacle, which is to abolish all motives and all consequences: what matters is not what it thinks but what it sees.
Next, the Jansenists were a Christian Catholic order, in 17th century France. They were involved in a continuous quarrel with the Jesuits of the day. The latter accused the Jansenists with heresy, on the grounds that the Jansenists held that God's Grace was given (if at all) deterministically, not influenced by the Free Will. Ultimately, the Jesuits managed to get the Jansenist doctrines condemned by the Pope. And when the Jansenists evaded the papal bull, and did not give up their teachings, their order was dismantled by force.
The Jansenists, on their part, accused the Jesuits with lax morality. The Jesuits were accused with relying on explicit and elaborate sophistical arguments to justify "usury, homicide, regicide, lying through 'mental reservation', adultery and loss of virginity before marriage". The Jansenists themselves were moral puritans. In fact, the term "Jansenist" became a synonym for "puritan".
Tying the two threads together, I think that Barthes may have been using the word "jansenist" in the latter sense:
Jansenist -> puritan -> pure -> genuine
That is to say, that the common form of boxing, unlike the common form of wrestling, was a "Jansenist", that is a pure, genuine sport.