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Dupuy will coach the backs and Azam the forwards and alongside John Haggart (defence) and Tristan Sharp (physical training) complete New Zealand coach Greg Cooper's backroom staff.
Former scrum-half Dupuy, 33, played for Stade from 2009 after stints with Biarritz and Leicester before retiring.
Prop Azam, 42, spent his playing career at Clermont and Gloucester, before a coaching role Toulon from 2011, followed by Lyon and Oyonnax.
Stade Francais have come through a chaotic season during which their very existence was under threat until a proposed merger with Paris rivals Racing 92 fell through.
Argentine coach Gonzalo Quesada left at the end of the season in which the club won the Challenge Cup.