By RAW, the net returns by itself to its wielder, though its unclear if the target is still restrained. However, the target is likely not restrained long enough to benefit the wielder.
net weapon states
Special. A Large or smaller creature hit by a net is restrained
until it is freed. A net has no effect on creatures that are
formless, or creatures that are Huge or larger. A creature can use
its action to make a DC 10 Strength check, freeing itself or another
creature within its reach on a success. Dealing 5 slashing damage to
the net (AC 10) also frees the creature without harming it, ending the
effect and destroying the net.
so, a creature is restrained until it is freed, as per the net description.
Returning Weapon states
This magic weapon grants a +1 bonus to attack and damage rolls made
with it, and it returns to the wielder's hand immediately after it
is used to make a ranged attack.
so, the weapon ('it') returns to the wielder after the attack is made. This means we need to refer to the Player's Handbook, chapter 9 (Combat), section - Making an Attack, specifically, Resolve the Attack
You make the attack roll. On a hit, you roll damage, unless the
particular attack has rules that specify otherwise. Some attacks
cause special effects in addition to or instead of damage.
In this case, the net inflicts a condition instead of causing damage. Once the condition (Restrained) has been caused, the attack is complete, and the net can return to its wielder.
The question is, does the net returning to its wielder (leaving the target) count as 'freeing' the target?
The net lists two methods of freeing, a Strength check, or a slashing damage attack; but, it does use the word 'can' in reference to the check, indicating an option; and, it does not say these are the only methods, so we can consider other ones.
Because the net starts as non-magical, and Returning Weapon only grants the ability to return, no other magical properties, we can apply real world understanding.
Absent of magic, a net can only apply it properties while on a target. Because Returning Weapon removes the net from the target, it is no long on the target, which means the Restrained condition it causes can no longer apply.
This means that Returning Weapon would end the restrained condition, thus preventing preventing the only reason to use the net weapon in the first place.