In mineral processing, froth flotation is based on recovering valuable mineral particles by means of the overflowing froth. Industrial-scale froth flotation cells are typically equipped with optical measurement systems, which monitor the bubble sizes and flow velocities at the froth surface. However, the velocity profile of the overflowing froth underneath its free surface is not accessible by optical observation. The present study combines X-ray radiography and particle tracking velocimetry in a laboratory-scale experiment aiming to measure local flow velocities within an optically opaque foam at a weir, which here describes a one-sided horizontal overflow. For this purpose, we prepared custom-tailored tracer particles: small 3D-printed polymer tetrahedra with tiny metal beads glued to the tetrahedral tips. In parallel to the velocity measurements by means of X-ray particle tracking, we determined the liquid fraction of the overflowing foam by electric conductivity measurements using electrode pairs. The experiment was performed with aqueous foams of two different surfactant concentrations but similar bubble size range and superficial gas velocity, yielding around 10% liquid fraction near the weir. Employing the particles as tools for flow tracing in X-ray image sequences, we measured the velocity profile in vertical direction above the weir crest and found that the maximum velocity is reached underneath the free surface of the overflowing foam.