For example, the ageing Earl of Crawford and Balcarres (1871–1940), a snob, thought him "vain as a peacock and all the mannerisms of a petit maître [in the sense of a dandy or fop]".
The passage uses this description to portray the Earl's opinion of the subject. The Earl was known for his snobbish nature and considered this individual to be vain and overly concerned with appearances, which is similar to a "petit maître".