The largest factor is arguably the demise of Louis XIV, who ruled and lived so long that both his son and grandson pre-deceased him. Louis XV was twelve years old and this a Regency was set up where Louis XIV's nephew d'Orleans was the nominal leader but de Maine an illegitimate son (one of many illegitimate children) held the true power. Thus, even as Orleans took power, it was largely governing through agreements and primarily concerned itself with internal finance reforms and upholding the peace, including alignment with Great Britain, Dutch Republic and Austria to check Bourbon Spain's ambitions in the Mediterranean (which saw significant changes at the end of the Spanish War of Succession).

Further, Louis XIV and Philip V's rule saw significant curtailment of noble and parliamentary powers in France and Spain. And of course, Louis placed a Bourbon in place of Habsburg Spain. Thus, even if the Regency was contentious there was no civil war.

GB and Spain did see enmity in the 19th century as Spain supported the Jacobites, but this came to nothing. Part of this was George I's massive failure through the South Sea Company, which bubble burst and made George and his ministers extremely unpopular.

Austria's main interest in this time were power projection in the Mediterranean and in the Low Countries via the Oostende company.

So 1720s was a bit of a breather for everybody following Louis XIV's aggressive domestic and foreign policies, and other great powers had either significant internal issues or focused their foreign policy away from continental Europe.