We apply the Lifshitz theory of dispersion forces to find a contribution to the free energy of peptide films that is caused by the zero-point and thermal fluctuations of the electromagnetic field. For this purpose, using available information about the imaginary parts of the dielectric permittivity of peptides, an analytic representation for permittivity of a typical peptide along the imaginary frequency axis is devised. Numerical computations of the fluctuation-induced free energy are performed at room temperature for freestanding peptide films containing different fractions of water, and for similar films deposited on dielectric (SiO_{2}) and metallic (Au) substrates. It is shown that the free energy of a freestanding peptide film is negative and thus contributes to its stability. The magnitude of the free energy increases with increasing fraction of water and decreases with increasing thickness of a film. For peptide films deposited on a dielectric substrate, the free energy is nonmonotonous. It is negative for films thicker than 100nm, reaches the maximum value at some film thickness, but vanishes and changes its sign for films thinner than 100nm. The fluctuation-induced free energy of peptide films deposited on metallic substrate is found to be positive, which makes films less stable. In all three cases, simple analytic expressions for the free energy of sufficiently thick films are found. The obtained results may be useful to attain film stability in the next generation of organic microdevices with further reduced dimensions.