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.