en.wikipedia.org/wiki/July_Revolution

This caption misstates the political outcome of the July Revolution.

A French Senate history page says the "Trois Glorieuses" of July 1830 ended the regime of Charles X and put Louis-Philippe, duc d'Orléans, on the throne. In other words, the result was the July Monarchy, not a republic.

An official art-history analysis of Cogniet's Scène de Juillet 1830, dit aussi Les Drapeaux explains that the work evokes the replacement of the Bourbon white flag by the national tricolour after the July days. That same source explicitly ties the image to Louis-Philippe and the Monarchie de Juillet. So describing the painting as showing a transition into a French Republic is inaccurate.

This sentence is chronologically wrong.

The French Senate's history page on the Charter of 1814 says Louis XVIII granted the constitutional charter on 4 June 1814. But the Congress of Vienna did not begin meeting until late summer / September 1814. Since the charter already existed months before the Congress assembled, the Congress of Vienna could not have been what "forced Louis to grant" it.

Whatever the broader diplomatic pressures on the Bourbon restoration, the specific claim that the Congress forced Louis to grant the Charter of 1814 is contradicted by the dates.