As a first name, "
Bruce" in French is
Bruce; just another of the many foreign borrowings the French have made in the last few decades. You really don't see much occurrence before the early 1980s, then a spike. Influence of
Bruce Lee or
Bruce the Olympic guy or
Bruce Willis...?
To double check, I Googled on "the history of Scotland" in French. The French texts all show
Robert Bruce as "
Robert Bruce." And the nationalistic French are very likely to Francicize a name in a historical context if there is a French equivalent; apparently there is not.