Gallicanism, initially most prominent in the 17th century in France, was the ʻtendency to enlarge the prerogatives of a national church—in the particular case, of the church of France—and to restrict proportionately the authority of the Holy See.ʻ ( W. Addis and T. Arnold. A Catholic Dictionary. , 1887)
In 1682 some French Clergy convened the writing of the ʻGallican Articlesʻ which clarified their position. Their most sticking article, which still rears its head today in the liberal factions of the those who claim to be Catholic, is the concept that Papal Power (in matters of Faith and Morals) is not absolute and that “The Pope has the principal share in questions of faith; his decrees regard all the churches and each church in particular; nevertheless his judgment is not irreformable, unless the consent of the Church be added.” (ibid)
Gallicanism was condemned by several Popes including Alexander VIII in his ʻInter multiplicesʻ (Aug. 4, 1690) Clement IX, and also Pius VI.
Furthermore, with the Vatican I definition of ʻPapal Infallibilityʻ it was declared dogmatically that "the decisions, ex cathedra, of the Popes are “of themselves,” that is, without the intervention of a further authority, immutable and not by reason of the assent of the whole Church, as the Gallicans taught" (Ott, Ludwig. FCD, 1957.)
Today this heresy often manifests its ugly head through the concept of papal teaching NOT being binding because the ʻSensus Fideiʻ (sense of the Faithful) has not accepted it. Some hold that if a bulk of Catholics DO NOT accept a particular Papal teaching, then it is NOT something we are bound to . . . . This is often the favored heretical reasoning of cafeteria catholicism.
A proper understanding of the ʻSensus Fideiʻ would be that those who deny a Papal definition would ipso facto NOT be a part of the true Catholic Faithful ʻSenseʻ they claim to represent.