Hawkbill seems likely to return to France for his next outing after getting back to winning ways at Newbury on Saturday.
Last year's Coral-Eclipse winner had his pipe-opener in the Prix Ganay before gaining his first win since the Sandown Group One.
Stepping up to a mile and a half appeared to suit and he yet again proved his effectiveness on soft ground.
"We know that he prefers soft ground, so we will be looking next to the Group Two Grand Prix de Chantilly (June 4). Obviously, we will be constantly watching the weather," trainer Charlie Appleby told www.godolphin.com
"If he can run at Chantilly, we might then give him a little summer break and bring him back in the Autumn, when there is a better chance of getting his ground."