Guillaume was born in Paris, France. His father was a lawyer from Normandy who had moved to the French capital. While still young, Guillaume lost his hearing, which may have motivated him to focus entirely on science. He never attended a university, but was able to study mathematics, the physical sciences, and celestial mechanics. He also spent time studying the skills of drawing, surveying, and architecture.

He died in Paris, France.

He was supported in his research career by the government, and was employed in various public works projects. Among his contributions to scientific instrumentation were improvements to the barometer (1695), hygrometer (1687), and thermometer (1695), particularly for use of these instruments at sea. He also demonstrated an optical telegraph and proposed the use of his clepsydra (water clock) for keeping time on a ship at sea.

Amontons investigated the relationship between pressure and temperature in gases though he lacked accurate and precise thermometers. Though his results were at best semi-quantitative, he established that the pressure of a gas increases by roughly one-third between the temperatures of cold and the boiling point of water. This was a substantial step towards the subsequent gas laws and, in particular, Charles's law. His work led him to speculate that a sufficient reduction in temperature would lead to the disappearance of pressure. Thus, he is the first researcher to discuss the concept of an absolute zero of temperature, a concept later extended and rationalised by William Thomson, 1st Baron Kelvin.

In 1699, Amontons published his rediscovery of the laws of friction first put forward by Leonardo da Vinci. Though they were received with some scepticism, the laws were verified by Charles-Augustin de Coulomb in 1781.