We analyze the performance of code division multiple access (CDMA) systems with multicarrier (MC) that employ random spreading sequences in downlink frequency selective fading channels. We obtain the probability density function (pdf) of the multiple access interference (MAI) of CDMA systems and extend the results to MC-CDMA systems to determine the pdf of MAI, inter-carrier interference (ICI) and noise in terms of the number of users, the spreading factor, the number of sub-carriers and frequency offset. The results show that the effects of frequency offset vary with system loading. We consider the synchronous downlink of cellular MC-CDMA and derive a Gaussian approximation of the MAI and ICI to reduce the computational complexity in calculating the bit error rate (BER). The accuracy of the Gaussian approximation is examined by computer simulations.