The incident happened on the A905 Wholeflats Road near Gate 10 at Ineos in Grangemouth at 5pm on Saturday, April 23.
Police in Forth Valley Division are appealing for the man to come forward as a witness.
A Volvo V60 car was travelling on the A905 when it moved across the carriageway, mounted a pavement and narrowly avoided a man who was walking in the area.
The man was carrying golf clubs at the time and, while he was uninjured, officers now wish to trace him as part of their ongoing investigation.
A 43-year-old man has been charged in connection with this incident and will appear in court at a later date.
PC Scott Kirkpatrick, of the Road Policing Unit, said: “I am appealing to this pedestrian or anybody who witnessed the vehicle driving on the pavement to contact police immediately.
“In addition, anyone with any further information that can assist with our inquiries should come forward.”
Those with information can contact Police Scotland on 101.