Given a discrete time sample X_1,... X_n from a Lévy process X=(X_t)_t≥ 0 of a finite jump activity, we study the problem of nonparametric estimation of the characteristic triplet (γ,σ^2,ρ) corresponding to the process X. Based on Fourier inversion and kernel smoothing, we propose estimators of γ,σ^2 and ρ and study their asymptotic behaviour. The obtained results include derivation of upper bounds on the mean square error of the estimators of γ and σ^2 and an upper bound on the mean integrated square error of an estimator of ρ.