He co-authored the section on comparative anatomy with Félix Vicq d’Azyr for the Encyclopedie Méthodique and was the founding secretary of the Société Philomatique.
The expedition visited Tenerife, Cape of Good Hope, Van Diemen's Land (Tasmania), New Ireland, Admiralty Islands, Ambon, Esperance Bay (Western Australia), Van Diemen's Land again, Tongatapu and Balade (New Caledonia) before disintegrating on royalist and republican lines in the Dutch East Indies on receiving news of the execution of Louis XVI.
Riche appears to have been consumptive and sought appointment as a naturalist on the Espérance because he believed the sea air would benefit his condition.
He was allowed to sail for the Ile-de-France (Mauritius) on the Scagen on 18 July 1794 (in company with Willaumez, Legrand, Laignel, Ventenat and nineteen other crew members).
Alas, the Dutch ignored his requests and he departed Batavia again on 29 March 1795, on the Nathalie, but nevertheless after having secured the release of Jacques Labillardière, the artist Jean Piron and some fifty other crew members from the original expedition.