For starters, in the Regency period of England, Jane Austin's era, women did not take part in sporting events as we understand them today. There were no women's basketball teams, cricket teams etc. P.E. was not taught in school.
So, women were to stay at home, tend to home making tasks such as wash-day, cooking, child rearing etc. Women were allowed to take the air by walking or bicycling. Women who were part of the peerage (royalty) could be quite accomplished horse riders and might participate in the fox hunt. The country dance was also a way that women might be active.
Men on the other hand had a wide variety of sporting events with which to pass the time. The pugilistic art (bare knuckle boxing) or as some aficionados called it, the sweet science, was very popular among the lower and middle class males. The poorer men and boys found a way to advance their living by winning at boxing events (which were illegal and often held in secret locations throughout the rural countryside near London and Great Britain). Other sporting pursuits that men engaged in would be golf (gentlemen only ladies forbidden), rowing, swimming, running, etc. Most sporting events were exclusive and required admission to a club, a price that many of the working class and poorer persons could not afford.
Women and men did not swim or "take the waters" together in mixed company as a general rule. Women wore full coverage "neck to ankle" bathing costumes to the shore, and were carried into the water by young men who watched over the ladies to be sure they did not drown.
Activities that men and women engaged in together included dancing, walking, bicycling, and croquet as well as lawn tennis which was a much slower game than the tennis game we know today.