If you go all the way back to the ancient Greeks, you'll see that they liked to start poems with something called the Invocation to the Muse. Homer (the original one, not the guy who coined "D'oh!") would open his poems by calling to the Muse to sing through him. It's kind of a humility thing—Homer and his fellow ancient bards weren't about to tempt the Fates by suggesting that they came up with something brilliant without a little help from divine forces.

The opening of the Intro to the Treaty of Paris does something similar:

In the name of the most holy and undivided Trinity. (Intro.1)

It would be tempting to call this a religious document because it has a reference to the Christian God, but that would be like calling McDonald's a toy store because of the prizes in Happy Meals. It's a side-note, not the main attraction.

Back then, it was almost a reflex action to include at least a passing reference to the divine. Without it, the treaty would have looked kind of uncouth and improper. The Treaty of Paris, therefore, mentions God in the same offhand way that most people say, "God bless you" after you sneeze.