When is the perfect moment to introduce eggs for a pale French omelette, based on butter condition?

Just as the butter's initial bubbling subsides.

Butter acts as both a cooking medium and a visual thermometer for managing heat, especially when aiming for the characteristic pale color of a French preparation. When butter is first added to the hot pan, it melts and begins to bubble and crackle due to the water content evaporating. The ideal temperature window for the eggs is precisely when this initial energetic bubbling ceases, indicating the surface heat is stable and hot enough to begin cooking the eggs quickly, but not so hot that it will immediately cause scorching or browning. If the bubbling stops and the butter starts taking on any color, the temperature is too high for a no-color result.