There was several evolutions during the period.

Linear advance was usual for french royalist army, who also experimented column moves. It did not fit the badly trained revolutionary french, who adopted column for quick moves on the battlefield (and also to rally willing, but often panicked units). The final move could be to deploy in line, for a firing contest, or assault in column to overwhelm the thinner ennemy line.
Skirmishers were added, I don't know exactly when, to screen the vulnerable column, disorder the ennemy line (who was not supposed to fire salvo on such small target), aim at targets of value like officers and artillery.

Also, organisation in France evoluted from wings or columns, with a multiplicity of ad-hoc responsibles, to brigades and divisions, later corps, with simpler chain of command of perennial group of units, making the evolution on battlefield easier to manage. The highest point was probably Auerstaedt, when well-trained Davout's units could alternate colum, line, square while under fire.

Monarchist armies rather used thin line of trained professional. They were effective against the early revolutionnary armies, but too static against the faster, more articulated late revolutionnary and french imperial armies.
Austrian had also massive full square, elaborated against the Turks, who used lot of cavalry and poor musketry. This did not suit against much more effective french fire.

Learning from defeat, monarchist armies developed divisions and corps, skirmishers, and popular levies, easier to manoeuvre in column than line. Against declining training level of french imperial units, it proved effective enough.

The exception was the British army, a smaller expeditionnary corps, who introduced skirmishers but kept the thin line of professional soliders in mostly defensive battles (with the exception of Salamanca and Vittoria). It proved very effective against french column, denying them the time to deploy in line at final step of the assault. But much less in offensive action, like Roliça, Redinha, or last stage of Salamanca against 6th Corps. Also, static line was under threat of turning move, like at Albuera and Fuentes de Oñoro.