The best example I can think of off the top of my head is the Kingdom of Bhutan, which adopted (in its Constitution, no less) an official measure of "Gross National Happiness" as the measuring stick for its policies rather than any purely economic model like GDP. There are government employees who go around the country with a surprisingly long survey that asks citizens all kinds of questions about their daily lives and material well being in an attempt to measure GNH, but the measure is still largely aspirational. When I was last there, it was the subject of some ambivalence in what is still a very poor, very small, very rural country: as one particularly salty fellow told me over drinks in Thimphu "GNH? It stands for Government Needs Help."

While I cannot speak to France, in the US Declaration of Independence the stipulation is not for the purpose of making possible happiness, but the Pursuit of Happiness, a distinction that may seem minor, but in the minds of the Founding Fathers, was important: the thing that provides happiness is different for every person, so the government's responsibility is not to provide happiness, but to ensure that each individual has the freedom to pursue the thing that they believe will provide happiness. therefore, at least in the mind of the Founders, the measurement of happiness is not relevant to the government, just the measurement of freedom.

An excellent read on the subject can be found in The Summer of 1787: The Men Who Invented the Constitution by David O Stewart (while the book focuses not so much on the Declaration, but on the drafting of the constitution) 1776 by David McCullough may cover it in more detail, but also covers the war in great detail. Forgive me, it has been a long time since I read 1776