Found out (spoilers)

Remember that Antoine tried to kill himself by taking his mother’s pills? The doctor treated him, so he must have deduced that for a well-adjusted boy to want to kill himself, he must have had a very good reason. He put two and two together and concluded that Antoine must have been involved in the disappearance of the younger boy somehow.

The watch was Antoine’s. Remember how he used it as an alarm clock to wake up? And then after the accident he realises it’s not on his wrist anymore? That was shown a couple of times. When Kowalski saw him cross the road and hide, he stopped the car and went looking for him. He must have found the watch and picked it up, probably to return it to Antoine – but then when it turned out that Remy had disappeared, Kowalski kept his mouth shut so as not to bring suspicion to the son of the woman he loved.