Despite efforts by an umpire, a former policeman, and other players to revive the father of five-year-old twin girls, French did not recover from a suspected heart attack.
Colleagues at the club paid tribute to French, a management accountant, who opened the batting.
Alan Wellman said: "Shaun was a competitive sportsman who enjoyed life. He was a big hitting batsman who had all the shots and he could win a game on his own.
"He was tired when he came into the pavilion but he drank a cup of tea. He had put his pads on to keep wicket when he collapsed.
"We have cancelled all our games until after his funeral next week."