Linearity with Difference Period in Fourier Transform
Continuous time Fourier transform does not require the signals to be periodic, and therefore the linearity assumption holds. CTFT is a linear operator.

Furthermore, if you mean CT Fourier series, which require that both signals to be periodic by (a common period) $T_0$, that's also linear.

But if input signals have no common periods, then you cannot apply the linearity test for CTFS.