Je ne peux pas arrêter de les regarder is correct French but probably not what you actually mean.

Usually, in English I can’t stop means I cannot refrain myself from doing something, e.g. I can’t stop smoking or I can’t stop sleeping do not mean you are smoking or sleeping 24 hours a day but just you cannot quit smoking or you cannot stay awake while you should.

If this is what you want to express about the paintings, the closest and most idiomatic way to say it in French would be:

Je ne peux pas m’empêcher de les regarder, tes peintures (ou tableaux).

You have multiple ways to say it :

« Je ne peux pas m’arrêter de regarder tes peintures. » (When you see a painting, you stay in front of it for a very long time)

« Je n’arrête pas de regarder tes peintures. » (You (very) often look at them)

« Je ne peux pas m’empêcher de regarder tes peintures. » (When you do something else, you want to see again his/her paintings)

In your particular context involving not being able to take your eyes off these paintings (and where I think you might be expressing a sort of loving [and perhaps flirtatious?] adoration of not just the art work but of the artist as well), you could perhaps wax slightly poetic and use the notion of:

ne pas quitter des yeux/du
regard

− Ne pas quitter des yeux, du regard qqc. Suivre quelque chose des
yeux, du regard. Chacun d’eux tient en ses mains un cahier de musique
qu’il ne quitte pas du regard (P. Lalo, Mus., 1899, p. 334).” (from a
remark under CNRTL’s definition II. B. -1.- b) of “quitter”)

I can think of three introductory phrases to use with “ne pas quitter des yeux/du regard” that you could use to convey the notion of your “incapability”:

“Je ne peux pas,” “Je n’arrive pas à,” and “Je ne parviens pas à,”
the last one being a bit more “wordy” and perhaps a bit more “rich” and therefore perhaps a bit more suitable than the first two if you are, in fact, trying to “touch” the artist’s heart and not just trying to state a dry fact to him/her.

With all these conjectures in mind, I would therefore suggest:

Je ne parviens pas à les quitter des yeux/du regard, tes peintures.

Or without the preceding “les” and the comma, which I personally like as I think they add more emphasis to “tes peintures”:

Je ne parviens pas à quitter des yeux/du regard tes peintures.

Otherwise, your suggestion is nearly perfect, lacking only the reflexive pronoun “m'” before “arrêter.”

Je ne peux pas arrêter... is grammatically correct but denotes a literal lack of capacity rather than a figurative strong attraction.

And Je ne peux pas m'arrêter... would not really be idiomatic in that case. I’d use it to emphasize the length of time of an action (je ne pouvais pas m'arrêter de rire) but not its cause.

Instead I would say

Je n’arrive pas à détacher le regard de tes peintures

or the more familiar

Je reste scotché à tes peintures