As far as I can tell? Nothing.
The feat doubles numeric measurements of the spell's area. Line spells don't have numeric measurements of area. They affect 'squares the line passes through', and they extend 'to the limit of the spell's range'.
If we take Lightning Bolt as an example:
Range: 120 ft.
Area: 120-ft. line
Well, there is a numeric measurement of area listed here - 120-ft line. So a Widened Lightning Bolt has a Range of 120 ft., and an Area of 240-ft. line.
And, of course:
A spell’s range is the maximum distance from you that the spell’s effect can occur, as well as the maximum distance at which you can designate the spell’s point of origin. If any portion of the spell’s area would extend beyond this range, that area is wasted.
So, a Lightning Bolt creates a 120 ft line. A Widened Lightning Bolt creates a 240 ft line, but 120 ft of that area (which would extend beyond the range of the spell) is wasted.
And, of course, the feat that increases range (Enlarge Spell) doesn't work on Lightning Bolt, since the range is not Close, Medium, or Long.
-Hyp.