The dog watches you as you move. To me, follow with his eyes sounds as if the eyes have been plucked out of their sockets. I still remember as a schoolboy in London being struck by the difference from English of the French phrase suivre des yeux.
I just googled your version and was unable to find more than a single entry that supports your it: When did your baby first follow an object with his eyes... which, however, has a special medico-physiological sense and does not sound at all odd to me. Admittedly in the well-known WW I recruiting poster with the caption Lord Kitchener Wants You, the eyes follow you (without with), to make you feel ashamed you are not in khaki. Watch would not be sufficient here.
Perhaps some native anglophone resident in the UK and not expatriate like both of us will kindly give us their opinion. I personally find that Spanish occasionally influences my English vocabulary and spelling, and I was once asked by an Englishman long resident in Provence if I had a good cart for my journey: he actually meant carte not charette. Amitiés, A.