Simply increasing contrast can work, but often creates problems with detail loss. In the case the OP describes the undesirable loss would be in the shadows; the desirable loss being the highlights gray/sepia tones.
A better control with which to make the adjustment is either Levels or Curves (Photoshop terms, most apps use similar). These can alter the highlights without a complimentary change in the shadows.
While I'm primarily a PS users (20+ years), I have found that
PhotoScape (freeware) is quite usable for basic changes. It has a Luminance Curve (click the "Bright, Color" button in the Editor to get the menu) control that is similar to PS's Curves and handles this type of edit easily. Dragging the upper right control on the curve allows you to adjust the highlight clipping (remove the gray/sepia background tone) and you can click and drag on the curve to bend it for further adjustment, again like PS's control.