I am not a native English speaker, I usually hear “something caught my eye” but never “something caught (both) my eyes”. This seems pretty strange to me.
Cambridge Dictionaries Online provide these examples but without any explanation
catch sb's eye
(i) to get someone's attention:
A sudden movement caught my eye.
(ii) to get someone's attention, especially by looking at them:
I tried to catch the waiter's eye, so we could order.
(iii) to be attractive or different enough to be noticed by someone:
It was the unusual colour of his jacket that caught my eye.
Why is only one eye ‘caught”? Doesn't something catch our sight? We normally see with both eyes, not with one.