Great-grandson of chancellor Séguier, brother of Pierre de Camboust and nephew of Pierre du Cambout de Coislin, on 20 June 1714 he composed a mandate denying the papal bull Unigenitus, which produced a sensation throughout the French church due to its author's personality, his diocese's importance and the sharpness of its condemnation of the bull, concealed beneath apparent submission to it. Louis XIV condemned the mandate by a Conseil decree of 5 July 1714 "as contrary to the acceptance of the Bull passed by the assembly of the clergy of France, and seeking to weaken or render useless the condemnation, both the errors contained in its 101 propositions, and the book that contains them". For refusing to seal this decree, chancellor de Pontchartrain was dismissed.
Bishop of France's most important stronghold, he relieved the city's burden of billeting soldiers by building a barracks on place du Champ at Seille - the barracks were bounded by 4 streets honouring the patron saints of Henri and his family (rue Saint Charles, rue Saint Henri, rue du Cambout and rue de Coislin). These barracks were demolished around 1930 to allow the construction of place Coislin (named after him), subsequently substantially rebuilt in the years after the Second World War to house a bus terminus, then a vast town-centre car park.