What is the title of this movie?

I watched this movie many, many years ago on TV and I'd like to see it again but I have no idea what the title is. I only remember fragments of the plot: 1) A woman travels back in time to medieval times, where she meets a boy I think it was a knight or a prince. 2) CPR did it, because he fell into a river and later in the story, kissed her on the pretext that it was RCP 3) The final was that again today and found another man Man.BB brought her in his study, where the wall was a large picture of a man. Turns out the man in the painting was the boy she met when she went back into the past, which proved to be the ancestor of man "B" or something. I hope it was not too confusing, I can not remember much myself, but I hope someone knows this film! Thanks in advance.

The Lakehouse Sandra Bullock and Keanu Reeves

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