Nonlinear optical properties of carbon nanostructures attract attention due to the unique response of these materials during interactions with ultrashort laser pulses. Here we probe the carbon nanocomposites mixed with epoxy resin in laser-induced plasmas using the high-order harmonics generation (HHG) method. We analyze the nanosecond pulses induced plasmas containing three carbon nanostructures (fullerenes, multiwalled carbon nanotubes and diamond nanoparticles) using 40 fs pulses propagating through these plasmas. HHG efficiencies in ablated graphite and nanocomposites are compared. We utilize two digitally synchronized (nanosecond and femtosecond) laser sources allowing for the HHG-based analysis of the evolution of different plasma plumes up to 10 µs delay from the beginning of ablation. The role of different carbon-containing nanocomposites is analyzed and the evidence for the presence of various nanomaterials in laser-induced plasma at the moment of propagation of the driving femtosecond pulses is demonstrated.