The trail departs from the park's southern trailhead on Interstate North Parkway. Extra parking can be found on the other side of the river at the Powers Island Trail. You would just need to walk over to the Cochran Shoals Trailhead along Interstate North Parkway.
More parking and information can be found here:
https://www.atlantatrails.com/hiking-trails/cochran-shoals-trails-along-the-chattahoochee/