Thank you Ashhar, your tip was the best :-) I've added a grounded gate FET
between the VCO and the PLL and now the receiver works as well with as
without the PLL circuit. I still have to adjust the loop filter because it
is not perfect; it can lock on the right frequency and keep it but the
output voltage of the filter doesn't look clean enough on the scope.

Thanks everybody for your advises, and cya ;-)

Damien