You do not need to be proficient in the weapon
Trip is a type of attack that says:
Requirements You have at least one hand free. Your target can’t be more than one size larger than you.
You try to knock a creature to the ground. Attempt an Athletics check against the target’s Reflex DC.
Tripping does not use a melee weapon attack roll, it uses your Athletics check instead, so you add your proficiency bonus in athletics. Then, if you want to use a suitable weapon for this, the trip trait for weapons says:
You can use this weapon to Trip with the Athletics skill even if you don't have a free hand. This uses the weapon's reach (if different from your own) and adds the weapon's item bonus to attack rolls as an item bonus to the Athletics check. If you critically fail a check to Trip using the weapon, you can drop the weapon to take the effects of a failure instead of a critical failure.
You are still not making a weapon attack, you are making a trip attack, that is an Athletics skill check, with the help of the weapon. You still use your Athletics proficiency bonus, not the weapon's proficiency bonus. That means, you do not need to be trained with the weapon (which would improve your weapon proficiency bonus) to make such a trip attack.
So, your wizard could take a guisearme into melee and try to trip someone with it. Let's hope they have a good Athletics skill bonus, and won't mind being stuck in melee.