But when I try to control the contactor and snubber network is connected, the contactor turn on, but when I turn it off, the contactor keeps load. Any ideas?
I suspect that your snubber on its own can supply a small amount of power to the load irrespective of whether the triac is connected or not. So, establish what you mean by "load" and determine what voltage the snubber forms with the "load" and, ask yourself if that is enough to activate the "load". I suspect it is.
It looks to me like the LC1D09P5 contactor coil only needs 7 VA at 50 Hz to hold the contacts close so, if this is your load then, quite possibly, the snubber will keep it powered.
You have the additional effect of the contactor coil inductance and snubber capacitor being in series and potentially drawing significant current when the triac is unpowered. This is due to series resonance so, you might consider using a lower value capacitor in your snubber to partially avoid this effect.
But, the problem only really occurs when the triac turns off and, this only happens when the contactor coil current is quite low in the AC cycle - this is how a triac works - so, you should benefit from this fact and use either no snubber at all or, a snubber with a higher impedance (lower capacitance). Try a 10 nF snubber.
Without knowing the contactor coil's inductance you are in the dark so, to design the snubber correctly you should contact the supplier/manufacturer.