Magneto-optical information storage has been a hot research subject for several years. FePt exhibits abundant physical properties and has received much attention as a candidate material. Its alloy film with perpendicular anisotropy and small grain size has important applications in magnetic recordings due to the large intrinsic magnetic anisotropy which ensures long-time thermal stability of nanometer sized bits. However, the large coercive field of FePt is a significant factor that hinders its application. As is well known, the magnetic anisotropy in FePt alloy can be precisely modulated by carbon-doping, and as a result, the coercive field of FePt film can be modified effectively with the carbon dopant. On the other hand, the microscopic mechanism of magnetic storage relies on the motion of spin system. Ultrashort femtosecond laser has been demonstrated to be a very effective tool to investigate the dynamical coupling among different degrees of freedom, such as electron, spin and lattice in a ferromagnetic film. The research on spin dynamics has become a new frontier of condensed matter physics, which is crucial for ultrafast magnetic recording materials. In this work, by using the time-resolved magneto-optical Kerr effect spectroscopy, we study the ultrafast spin dynamics of two FePt alloy films with different carbon dopants under the applied magnetic field along the film surface. The FePt alloy films with different carbon dopants are fabricated on silicon substrates by the sputtering method. The main experimental findings in this work are as follows. (i) The transient Kerr signal is linearly proportional to the magnetization with the magnetic field up to 0.8 T, while the transient reflectivity of the film is independent of the applied magnetic field. (ii) For FePt alloy films with different coercive fields, it is found that the demagnetization time of the film with smaller coercive field is significantly faster than that of the larger counterpart: the former shows 0.8 ps demagnetization time, and the latter has a magnitude of 1.2 ps. The demagnetization times for both soft and hard magnetic films are independent of the applied magnetic field. (iii) With ultrafast laser pulse radiation, we observe the propagation of acoustic phonon with a resonance frequency of ～ 49 GHz, and the frequency of the acoustic phonon is independent of the applied magnetic field. From the above, the spin dynamics of the samples shows strong correlation with carbon-doping. Our experimental findings are desired for basic research as well as for the design and development of novel magneto-optical devices.