A fuel injector system for injecting fuel into a turbomachine combustion chamber, the system comprising first and second fuel injectors wherein the first injector (22) is positioned in the center of the injector system (20) so as to inject a first fuel spray (42), and wherein the second injector (28) surrounds the first injector in such a manner as to inject a second fuel spray (48) of generally annular shape around the first fuel spray. The injector system further comprises an air admission duct (22) with outlet orifices (62) opening out between the first and second injectors so as to create a separator air film (f1) between the respective combustion zones of the first and second fuel sprays.