Someone Evil's answer mostly covers the rules as written.
Rules on unseen attackers
That being said, if your DM wants to follow the RAW as much as possible while still allowing you to pull this off somehow, I suggest using the rules on object AC/HP and the rules for unseen attackers (PHB, p. 195):
When you attack a target that you can’t see, you have disadvantage on the attack roll. [...] If the target isn’t in the location you targeted, you automatically miss, [...] When a creature can’t see you, you have advantage on attack rolls against it.
When attacking through the wall, you would make a normal attack roll, since you being unable to see the target and the target being unable to see you cancel each other out (having both advantage + disadvantage = normal roll).
Rules on object statistics
Regardless of the material the wall is made out of, the DMG has rules on object AC and hit points on p. 246; paper (for Japanese-style paper walls) has an AC of 11, wood has an AC of 15, and stone an AC of 17.
A paper wall would likely have 5 hit points (being "fragile", see DMG p. 247), while a stone wall would have 27 hit points (being "resilient"). A wood wall could have either.
Depending on the material, your DM can decide that the object has damage vulnerabilities or resistances (see DMG, p. 247, "Objects and Damage Types"). For instance, a paper wall might be vulnerable to slashing and fire damage, while a stone wall could be resistant to slashing and piercing damage.
Those rules apply RAW as well, except you technically have to use a number of attacks on the wall until it is destroyed, before you can use a separate attack on the enemy behind the wall.
Houserule examples that are as close to RAW as possible
The closest to RAW would therefore be to grant you advantage on the second attack (assuming you can smash through the wall with your first attack), since your target didn't see you. This wouldn't technically be the case as it can see you once the wall is broken, but it's a minor change that's well within the DM's ability to grant advantage in certain situations. I'm not 100% certain it would be RAW, but it's at least debatable.
A more significant change (that is definitely not RAW anymore) would be to allow you to deal any excess damage from hitting the wall to the attacker. As an example, let's say you hit a paper wall with a Greataxe and get a 22 on your attack roll and a 13 on your damage roll. Assuming the attack roll is higher than both the wall and the target's AC, you would deal 10 damage to the target; 3 damage are required to destroy the wall, which I would consider a fragile large paper object (=5 HP) vulnerable to slashing, and the remaining 10 damage would hit the target.