The total and partial cross sections for the capture process C6++He+C5++He2+are computed at impact energy in the range 0.1-40 keV amu-1using the classical trajectory Monte Carlo (CTMC) method. Rate coefficients, which are used in practical applications, are estimated by assuming Maxwellian energy distributions for both incident and target ions, and are used to compute the intensity of the hydrogen-like carbon Lyman series lines in a fusion plasma. A comparison with the line ratios measured in a reversed field pinch device is made. It is shown that this charge exchange process is not likely to sensitively alter line ratios in helium fusion plasmas.