Intermediate-mass stars are often fast rotators, and hence are centrifugally flattened and notably affected by gravity darkening. To analyse this kind of stars properly, one must resort to 2D models to compute the visible radiative flux and to take the geometrical effect of the star inclination into account. Assuming a given stellar age and chemical composition, our aim is to derive the mass and rotation rates of main sequence fast rotating stars, along with their inclination, from photometric quantities influenced by gravity darkening. We chose three observables that vary with mass, rotation, and inclination: the temperature derived by the infrared flux method TIRFM, the Stroemgren c1 index, and a second index c2 built in the same way as the c1 index, but sensitive to the UV side of the Balmer jump. These observables are computed from synthetic spectra produced with the PHOENIX code and rely on a 2D stellar structure from the ESTER code. These quantities are computed for a grid of models in the range 2 to 7M_{sun}_ and rotation rates from 30% to 80% of the critical rate. Then, for any triplet (TIRFM, c1, c2), we try to retrieve the mass, rotation rate, and inclination using a Levenberg-Marquardt scheme, after a selection step to find the most suitable starting models. Hare-and-hound tests showed that our algorithm can recover the mass, rotation rate, and inclination with a good accuracy. The difference between input and retrieved parameters is negligible for models lying on the grid and is less than a few percent otherwise. An application to the real case of Vega showed that the u filter is located in a spectral region where the modelled and observed spectra are discrepant, and led us to define a new filter. Using this new filter and subsequent index, the Vega parameters are also retrieved with satisfactory accuracy. This work opens the possibility to determine the fundamental parameters of rapidly rotating early-type stars from photometric space observations.