The Racing Steps Foundation-backed driver, buoyed by his first championship victory at the last race at the Hungaroring, traded pole position in the early stages of the sodden first qualifying session with Hitech GP team-mate George Russell.
Both were split by the Prema Powerteam duo of Lance Stroll and Nick Cassidy in the final stages though. Stroll scored pole position with Cassidy finishing third.
Holding a three-place grid penalty for the opening race of this weekend, following a collision in Hungary, Russell will therefore begin from fifth position, elevating Cassidy on to the front row alongside his team-mate with Barnicoat moving to third position.
Later in the afternoon, Barnicoat went on to set a best time which was good enough for a ninth place start in race two, which will be headed by Russell from pole position. Based on second quickest times, Barnicoat will begin the final race, the blue riband Pau Grand Prix, from seventh.
“We just missed the ideal window a little in second qualifying,” Barnicoat said. “It was taking the car a long time to come on, but the pace in the car was still good. Every time I came over the line I was first or second, I was just very unlucky that George [Russell] backed right off making me do the same behind him.
"That meant that I didn’t get another lap to improve and I dropped from second all the way down. It’s frustrating, but the speed is there in the car for the rest of the weekend.”