According to the Life of Lieut.-Admiral de Ruyter by G. Grinnell- Milne the wounding of the admiral was kept secret not only from the French but from the ships of his own fleet (see p. 241). The wound was very serious, badly mangling his foot and breaking his shin. Captain Callenburgh took over command of the Eendraught when the admiral was wounded and conducted the battle with the admiral's advice, though he was prostrate. By 7 o'clock the French had been defeated and were fleeing. The Dutch gave chase by the light of the moon until 8 o'clock when an approaching storm required them to retire. There is nothing in the account in this book that the French knew that the Dutch admiral had been wounded.
The next morning the French headed for Calabria and Dutch decided to take shelter in the port of Syracuse.
Although at first it was thought he would survive, De Ruyter died of his wound about week after the battle, possibly of septicemia.
I also consulted the book "De Ruyter: Leven en daden naar berichten en afbeeldingen Van Tijdgenooten." by Michiel Adriaensz (1907) and the account in this book has no additional details over those given by Grinnell-Milne.