Usage of "Don't remember"

In my language I can say "I don't remember I've ever watched that film" or "Never in my life have I remembered watching that film" to suggest that as far as I can remember I've never done something, or in a stronger sense that I can recall I never did something.

Do you, as a native speaker, use "don't remember" in such sense? Otherwise, what is the natural way to put it across?

Edit: Thanks guys for your inputs, but I still have a question. Let's say somebody told you your friend Ken has a ring, but as far as you know or could recall he doesn't have one. My immediate response would be like "Oh? But I don't remember he ever has a ring" Would this be okay? I know how it sounds, it may sound like I just forgot the fact that he has a ring. What would be a commonly used expression for such situation?

The first one is simply wrong. The second is grammatically correct but very awkward. You would say

"I don't remember ever watching that film."

and

"I've never watched that film in my life."

The second is more emphatic and sure-sounding. In the first, you're allowing for the possibility that you have watched it but can't remember doing so at the moment.

There is a closer use to your examples , but it may be only UK English, which has more circumlocution. Example .1. "I don't remember if ..."

I don't remember if I've ever watched that film: the book was so vivid.
I don't remember if Jeremy was there; I only had eyes for his sister.

And .2. for the more emphatic sense: "I would have remembered."

I didn't see the film; I would have remembered.
The letter of warning/ apology/ resignation never arrived; I would have remembered.

which, for your example would be:

Never in my life did I see that film with [say, Jack Nicholson] the actor; I would have remembered.

Notice: "Never did I see... " (the restriction of diminished opportunity requires an inversion) is slightly more appropriate for portrait...

Dracula Ch16 Never did I see such baffled malice on a face, ...

Leigh Hunt - 1837 - Liberalism: Never did I see such a movement of generosity and gentleness in all affections , as these children evinced...

D. H. Lawrence (1885-1930) on James Joyce. Never did I see such apparatus got ready for thinking, ...

...but “Never have I seen ...” is more usual with landscape or where the gaze is held.

Old Man and the sea: Never have I seen a greater, or more beautiful, or a calmer or more noble thing than you, brother.

Conan Doyle: Never have I seen such a mixture of strength and beauty and grace.

But see the research by SevenSidedDie below which clearly shows "Never have I..." is preferable.