How Does Line Frequency Affect Coils of a Contactor?
An AC coil presents a specific impedance at a specific frequency.

\begin{equation}
X = 2\pi fL
\end{equation}
Where:

L = coil inductance in Henrys

f = frequency

X = impedance

Your contactor's coil is specified at 50-60Hz.  If you instead use 240Hz, then the impedance will be higher, and not enough current will flow through the coil to activate it.

X above can be substituted as R in Ohms law V=IR => V=IX to show how much current will flow.