The magnetic flux around a wire IS going from north to south. You can prove this by holding a small compass next to a straight, long wire carrying a direct current (DC) - the needle will point perpendicular to the wire no matter where you hold it. The only way to account for this is if the field lines go around the wire. Furthermore, a piece of iron placed next to the wire will become magnetized in the same direction as the field lines passing through it, i.e. perpendicular to the wire.
When you wind the wire on a solenoid, the magnetic contribution from each wire is in the same direction as all the others, so the field makes a bigger loop to include all the wires, eventually resolving as a large donut that passes through the middle of the solenoid, loops around through space and rejoins itself. The important thing is that magnetic field lines always form continuous loops.
Wikipedia: "magnetic forces can be understood by imagining that the field lines exert a tension, (like a rubber band) along their length, and a pressure perpendicular to their length on neighboring field lines. 'Unlike' poles of magnets attract because they are linked by many field lines; 'like' poles repel because their field lines do not meet, but run parallel, pushing on each other."
BTW, magnetic field lines themselves are NOT "Equal Potential Lines", they represent the direction of the field, not its strength. The strength of the field is represented by the spacing between the lines - in a stronger field, the lines are closer together. Each line represents a certain amount of magnetic flux (unit: Weber) and the spacing of the lines represents the magnetic flux density (Unit: Tesla = Webers per square meter)