Planteur has a long-term aim of the Red Mills Irish Champion Stakes after his third-placed finish in the Prix d'Ispahan at Longchamp on Sunday.
The Marco Botti-trained five-year-old was beaten just over a length by Golden Lilac and Cirrus Des Aigles.
He is next likely to run at Royal Ascot before being geared towards the Irish Champion Stakes at Leopardstown on 8 September.
Botti said: "He ran a great race and we were thrilled with him, it was a good performance."
Botti added: "The ground had just dried out a little too much for him or he might have won - we know he is better with a little bit of cut in the ground. Also, he could have done with a stronger pace.
"Christophe Soumillon rode him in France and said it was a very good run and that he could be effective over a mile or 10 furlongs. He's entered in the Queen Anne and the Prince of Wales's at Ascot.
"Frankel looks like running in the Queen Anne so that is something to consider. Long term, the Irish Champion Stakes looks the right race for him."