According to an article in French Wikipedia, this firm started at 2, rue d'Amsterdam, the same address as G Piprot, and was restructured between him and his brother-in-law in 1905.
The IRIS mark was already registered in the 1907 list. IRISA and IRISETTE were added by 1914, plus "as de coeur" and "as de pique" (ace of hearts and ace of spades) logos. By 1922 RP and FURIA had been added and the earlier marks dropped. Two RP cards are shown here with different logos.
By 1925 this firm had merged with Papeteries de Levallois-Clichy, which produced PC, REX and other marks. The merged firm continued to produce RP and FURIA cards.
www.cparama.com/forum/les-editeurs-parisiens says:
R. P., éditeur à Paris, 159, rue Montmartre. (initiales de R. Pruvost).
This may be the previous owner of the RP marque, though that list is only giving publishers which produced views of Paris.
Other IRISes
IRIS Verlag in Vienna published series of cards of film stars, using a number of different logos. This has its own entry on this site.
In more modern times, Théo Bachellery of Limoges has used an IRIS mark, as shown below, typically on coloured views.