What happens if a neutrino collides with an electron?

Quantum Mechanics does not use the term ‘collide’. It is better to use the terms ‘interaction and ‘Quantum scattered’. Two Quantum particles from the same range of possible Quantum interactions swap vector bosons and are scattered by that interaction.

Low energy Electrons interact with Gravity and Electromagnetism.
Neutrino can interact with Gravity and Weak force.

Gravity is the only possible interaction between Electrons and Neutrinos in the low-energy regime. Their Gravitational interaction with each other is negligible, if not zero. In normal everyday life, Neutrino does not interact with Electron.

High-energy regime
The ‘Electroweak Force’ is a unification of the weak and electromagnetic forces. Above the unification energy (246 GeV), Electrons and Neutrinos can interact via Electroweak interaction exchanging weak charge and electron-neutrino electric scattering. The Neutrino scattering area is extremely small, making it statistically unlikely that the interaction occurs. This interaction is possible to detect, and can be used to do Neutrino Physics (for example to test Solar Neutrino model), and research on Standard Model of Particle Physics.

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