"her dearly loved copy of the Pensées of the Abbé Fausse-Maigre"

The Pensées of the Abbé Fausse-Maigre appear to be a product of Stella Gibbons' fertile imagination, but she may have had in mind the Pensées of Blaise Pascal, the French 17th century philosopher. 'Fausse' translates as 'false', and  'Maigre' as 'thin', so Fausse-Maigre could be translated as 'falsely thin', a euphemism for 'fat', perhaps!

The Abbé's other (and more complex) work is The Higher Common Sense. There appears to be a novel by Arthur Henry, an American Writer of the late 19th and early 20th century, entitled  The Higher Common Sense: The Unwritten Law, but it is not clear whether this is in any way related to Gibbons' choice of title.