Learn French: J'ai mal à l'œil.

French doesn't usually use a direct verb for 'to hurt' in this context. Instead, you use the expression avoir mal à (to have pain at/in) followed by the body part. J'ai mal literally translates to I have pain.

Why does it use l'œil (the eye) instead of mon œil (my eye)?

When it is obvious whose body part you are talking about, French uses the definite article (le, la, l', les) rather than a possessive word like mon. Because you started with J'ai (I have), it is perfectly clear that you are talking about your own eye!

How would I say 'My eyes hurt' if both of them are hurting?

The plural of un œil (an eye) is highly irregular: des yeux (eyes). To say both eyes hurt, you must combine à and les into the plural word aux, making the sentence J'ai mal aux yeux.

How does l'œil relate to the verb voir from this lesson?

L'œil is the noun for the body part you use to voir (to see). A fun bonus phrase using this is un coup d'œil (literally a strike of the eye), which is the French way to say a glance or a quick look.