There are several reasons why we use ground planes. If the signal level is relatively low it might be more helpfull to use a ground plane.
The first reason is that we want a low impedance path for the ground signal so we know the ground potential is well defined all over our pcb.
We also want to signal loops to be as small as possible. Pouring a ground plane can help, but you should look at the return path of the signal through the ground plane to see wheter it is correct. This is especially important in highg current traces, but in your case as well, because a larger loop is more prone to pick up noise. As you can see below the loop for signal2 is a small as it can be, but for signal one you can improve it if you want, by routing signal 1 around the most left pad of the connector.
Furthermore we use the ground plane to shield from interference. By routing the signal between to parts of the ground plane it is most immune to those signals (as you almost have a coaxial cable, because it is shielded on both sides by ground). In your case it is poorly shielded because the ground plane is only on one side of the trace.
For RF pcbs people go to even further extent, by using vias to the ground plane on the other side to even shield that:
Although those points are in theory very usefull, it is not always possible and definitely not always needed for a good PCB. We always have other reasons at stake, like cost and pcb size. So use the things that you think are necessary for good signal integrity.
Personally I would maybe take the effort to make the loop smaller by rerouting signal one, but the ground plane on the other side seems optional to me.