How did the Chunnel tunnels stay lined up to meet in the middle?

Lasers. Due to the depth, GPS would be unsuitable. Instead, lasers where directed backwards through the tunnels from the massive tunneling machines and with extensive calculations, the tracking of the beam allowed the position of the machine to be determined over time.

Without digging into exactly what they did, I'd guess survey-grade GPS to plot the start points, and standard surveying techniques (lasers, nowadays) to keep track of the underground sections.

It's a bit more impressive that people managed this kind of thing in the past, before lasers and GPS.

The tunnel boring machines were guided and steered using lasers and hydraulic jacks.

According to the documentary, they used GPS