Having been involved in a French dog club (me with agility) but the club was originally a French equivalent of Schutzhund club, called French "Ring", I'd say that the temperament of a lab would make it difficult to progess past basic levels in Schutzhund. The obedience part and tracking would be easy but the attack part, well they are much more geared to working defence breeds like GSD, BSD, Dobbies etc, as it involves bitework. I'd be seriously disappointed if anyone considered our breed as a suitable breed for serious schutzhund or French Ring. A labrador is not a guarding breed and any inclination to bite, in an albit it controlled manner, other than carrying dead prey should be seriously discouraged and surely goes against the breed standard?
As I said, I used to be closely involved as an observer in French ring which is in many way much stricter than Schutzhund and I'd be horrified if I saw a lab taking part in competition.