"Wrong side of the road"! "Wrong lane" never refers to someone literally driving into incoming traffic, and we reserve "wrong side of the road" for the case where all the cars are going South and one is going North on the same side of the median. If clarification is needed, you could always use the more technical way to say it, "driving on the wrong side of the median". (The median is the dividing line between the two directions of traffic)
The case where one might use "wrong lane" could be something like, "I missed the exit to get to the mall because I was in the wrong lane".
Note: This is American English, where we drive on the right of the median. Other countries can differ.