The Newton’s rings are circular and the fringes in wedge shaped film are straight because :
1.The shape of the fringe depends on how the thickness of the air film enclosed varies.
2.In wedge shaped film the thickness of the air is constant over a straight line along the width of the wedge.
3.Hence the fringes are straight.
4.In a newtons ring set up the air film is enclosed below the convex lens. The thickness of the film is constant over a circle (or concentric circles) having center at the center of the lens.
5.Hence the fringes are circular.