Do you have the processing rules for marketing channels set up? Create Marketing Channel processing rules
If you do, you can break down all form submissions (however you have this tracked: event, pageview, etc.) by the last touch channel. This would tell you, of the form submissions, how many came via natural search, paid search, etc.
If you wanted to create a segment, you would use the same dimension, i.e. visits or hits where the last touch channel = paid search.