An on-camera flash is likely the least effective option here, but flash itself is not useless. The better approach is to use off-camera lighting so the light is placed near the couple and aimed from a flattering angle rather than from the camera position.

A practical setup would be two off-camera flashes, ideally with softening modifiers such as small softboxes or diffusion, and possibly a reflector if needed. That lets you light the couple separately from the dark room and wood interior.

If the venue is large or you want to preserve the ambient look of the staircase and room, you may also need a longer exposure for the background. In some cases, a composite can help: make one exposure for the scene/background, then another with the couple lit, and combine them later. This can also help keep lights out of the frame.

If you can’t add lighting, then yes: use the fastest lens you have, raise ISO, and use the slowest shutter speed they can hold still for—but off-camera flash is the stronger solution.