Bourdy, a three-time winner on the European Tour and runner-up at the Maybank Malaysian Open last month, fired nine birdies with bogeys at the 15th and seventh the only lowlights for the 29-year-old at Pula GC.
England's Danny Willett was second, with a bogey five at the 12th the only thing preventing him joining Bourdy in a share of the early lead.
Northern Ireland's Darren Clarke, who won the last of his 12 Tour titles in 2008, was third following a five-under-par 65. Bourdy said: "It's always great to hold a course record. It's very nice on Tour to get a score like this. I made nine birdies, only two or three mistakes but it was a wonderful day."
Clarke, the star of Europe's emotional Ryder Cup triumph at the K Club in 2006 and a vice-captain in the 2010 success at Celtic Manor, has dropped to a world ranking of 124 but, after following two birdies with two bogeys in his opening four holes, concluded his round with five more birdies to put himself in contention for a first victory since the KLM Open in 2008.
England's Matthew Nixon joined Clarke in a share of third place thanks to two birdies on his final three holes. Welshman Rhys Davies was a shot adrift in fifth after a 66, with England's Chris Wood, Scotland's Scott Jamieson, Argentina's Cesar Monasterio and South African Jaco van Zyl tied for sixth after 67s.
Colin Montgomerie had a round to forget with a seven-over-par 77.