Ground-based spectroscopic follow-up observations of the pulsating stars observed by the Kepler satellite mission are needed for their asteroseismic modelling. We aim to derive the fundamental parameters for a sample of 26 γ Doradus candidate stars observed by the Kepler satellite mission to accomplish one of the required pre-conditions for their asteroseismic modelling and to compare our results with the types of pulsators expected from the existing light-curve analysis. We use the spectrum synthesis method to derive the fundamental parameters like Teff, log g, [M/H] and v sin i from newly obtained spectra and compute the spectral energy distribution from literature photometry to get an independent measure of Teff. We find that most of the derived Teff values agree with the values given in the Kepler Input Catalog. According to their positions in the HR diagram, three stars are expected γ Dor stars, 10 stars are expected δ Sct stars and seven stars are possibly δ Sct stars at the hot border of the instability strip. Four stars in our sample are found to be spectroscopic binary candidates and four stars have very low metallicity where two show about solar C abundance. Six of the 10 stars located in the δ Sct instability region of the HR diagram show both δ Sct- and γ Dor-type oscillations in their light curves, implying that γ Dor-like oscillations are much more common among the δ Sct stars than predicted by theory. Moreover, seven stars showing periods in the δ Sct and the δ Sct-γ Dor range in their light curves are located in the HR diagram left of the blue edge of the theoretical δ Sct instability strip. The consistency of these findings with recent investigations based on high-quality Kepler data implies the need for a revision of the theoretical γ Dor and δ Sct instability strips.