Modern particle accelerators and their applications increasingly rely on precisely coordinated interactions of intense charged particle and laser beams. Femtosecond-scale synchronization alongside micrometre-scale spatial precision are essential e.g. for pump-probe experiments, seeding and diagnostics of advanced light sources and for plasma-based accelerators. State-of-the-art temporal or spatial diagnostics typically operate with low-intensity beams to avoid material damage at high intensity. As such, we present a plasma-based approach, which allows measurement of both temporal and spatial overlap of high-intensity beams directly at their interaction point. It exploits amplification of plasma afterglow arising from the passage of an electron beam through a laser-generated plasma filament. The corresponding photon yield carries the spatiotemporal signature of the femtosecond-scale dynamics, yet can be observed as a visible light signal on microsecond-millimetre scales.