The Olympic eventer fell at fence 20, an owl hole, on the cross-country at Le Lion d’Angers with Reinstated.
The pair were competing in the seven-year-old CCI2* class at the FEI/WBFSH world championships for young eventing horses.
The horse, whom William first competed in May 2014 at Chatsworth, was not injured in the fall.
The course was held for more than an hour while William received medical assistance before being transferred to Angers hospital.
“William has suffered a head trauma, but is otherwise fine. He is comfortable and stable under sedation and will be under constant observation,” read a statement on Saturday.
This morning (Monday, 19 October) a spokesman for British Eventing told H&H there was “no change” in William’s condition and that he remains “under observation”.
“William had a good night and remained stable and under sedation; he will undergo further tests later today,” the spokesman added.
“On behalf of the Fox-Pitt family and their support team at home, William’s wife Alice Fox-Pitt would like to express her thanks to everyone for their support and well wishes, it means a tremendous amount to them all that everyone is thinking of William.”
Alice has travelled to France to be with him.
Willliam, who currently stands at number three in the world eventing rankings, had already completed the course successfully on his first ride, The Soapdodger.
His last win was at the CIC3* at Hartpury in August with Bay My Hero.