I had the same problem.
So I made research. And here what I found.
At my website I disabled rest api one day.
And now I have error with Caldera forms – Unexpected token < JSON at position 0. It’s because wp-json is disabled.
So here what you must do.
Delete plugin or code (at functions.php) that disabled rest api. Then press “Save” at Settings-Permalinks. Now form will be sent.