The infinitive is definitely required for this meaning; but the tensed form goes is also correct. However, it means something quite different -- it means she said that he attends the cinema regularly.
I've seen the form "said he" a couple of times in literary works to express solemnity, but I don't think that applies here. When would you say "said he" rather than the common "he said"?
When would you use "said he"? - English Language & Usage Stack Exchange
He said, “ QQQ.” “ QQQ,” he said. “ QQQ,” said he. In particular, in what situations is the “inverted” VS 1 order of said he preferred over either or both of the two versions that use he said in the “normal” SV 2 order? Are these nothing more than three equal options that vary by individual writers’ personal tastes?
meaning - “He said, X” vs. “X, he said” vs. “X, said he” - English ...
He was saying adds the continuous sense to he said, it suggests that he spoke at length, and so "he is going to leave soon" is just a summary, not directly quoted speech.
What is the difference between "he was saying", "he says" and "he said"?
Replace the pronoun with a proper noun: 'I will!' said Sam. Notice that it sounds normal now. A hundred years ago it also sounded normal to say said he, but customs have changed; we no longer like to use inversion with pronouns. It sometimes sounds solemn because archaic language is often used for the express purpose of sounding solemn--but remember that you're reading Tolkien, who loved Old ...