The village's name would likely originate from the old name Haverec. However, etymologists are uncertain about the origin and meaning of the name. Some say it would mean Country of the hops, some other think it would mean cleared ground, and more recently a German line of thought associate it with a German word that could translate to wild ash tree.
Havré was a wealthy municipality from the 19th century to 1950, with forests, salt refinery, tannery, tabac fabric, gunpowder factory, glass factory, phosphate quarry, but mostly thanks to coal mines which employed more than a thousand people.
In 1960, after the last coal mine closed, the village became a commuter-town for people mainly working in Brussels, Mons, and Charleroi.
In the tertiary sector of the economy, Havré counts small and medium supermarkets, and there are retail and handicraft shops. Sport is also developed with infrastructure for tennis, football, and basketball.