This question could be answered a hundred ways, but just looking at the broad strokes you can make the argument that the napoleonic era defined warfare in Europe to the outset of ww1, not only in the tactical and strategic innovations, but also in ushering in the diplomatic age of Metternich, allowing the theories of clauswitz to be developed, introducing real war time footing for whole nations, in general terms having armies filled with soldiers that are fighting for a nation principally on a large scale.

Rewind a hundred years to the war of Spanish succession and you'll find the Duke of marlborough, generally considered one of the best military commanders in European history. The armies of this area took forever to march any great distance, took a day to assemble for battle, and were remarkably rigid. Marlborough fought very few pitched battles (blenheim, ramilles) and the size of his army was less than 100k soldiers with fewer than 100 field pieces. In many ways, armies remained roughly this size and composition through the beginning and middle of the napoleonic era. However, by the end of the area, as evidenced by the battle of Leipzig, armies were much larger and cannons were the absolute focal point (more than a half million men and 2000 field pieces were deployed over a battlefield stretching dozens of miles).

The causes for these various changes were many. For instance when the prussian army was crushed at the battle of Jena-auerstedt in 1806, the prussians realized how behind the times they were and embarked on a massive overhaul of their military (which took several years due to their humiliation from the treaty of tilsit that limited their army to 42000 men and bound them to fight for napoleon, causing the defection of much of its officer corps to Russia over the next several years). The main prussian army deployed in line and marched several miles to meet napoleon, which slowed them down and left their forward deployed forces to be picked apart by napoleon's much more mobile forces. This deployment and maneuvering in line was an 18th century tactic. Napoleon on the other hand had by this time organized his forces by the corps system, where marshals would command a portion of the overall force large enough to fight a pitched battle by itself for a day or more while the rest of the forces could catch up. Essentially his forces marched in a diamond arrangement with maybe 20,000 soldiers in each corps. When a corps made contact with the enemy, it could either overwhelm a small force, or deploy completely and act as the advance guard for the other three or four corps marching behind them. By marching in a diamond, any corps could be the advance guard or rear guard for the entire force, but the force could still be spread out to allow for maneuverability, foraging, etc.

Additionally, napoleon developed the attack column in contrast to fighting in line like the prussians. Rather than two or three ranks deep in line, napoleons columns could be 8 or 12 ranks deep or more, shortening their front (which could reduce firepower but was easier to maneuver) but adding shock force to a charge. There were very few full on bayonet battles in the napoleonic era. Usually one side would break and run if the charge threatened their lines.

The campaign before Jena was the ulm campaign, culminating in the battle of austerlitz at the end of 1805. Napoleon only deployed a little under 70,000 troops at this battle, compared to the almost quarter million deployed at leipzig in 1813. This battle is considered napoleon's finest, but the biggest takeaway was the brilliance of napoleon's merit based forces compared to the Russian force where the aristocracy comprised the mounted life guard. Napoleons cavalry simply outperformed the aristocratic Russian cavalry. This battle saw the effectiveness of attack columns marching up a long slope and crushing the center of the Russian line, and the Russian reserves, their picked troopers, unable to retake it. The battle for the center was horribly bloody, seeing both of the commanding French generals receiving severe wounds. This campaign and the campaign in Prussia was the last in which cannon were not the absolute key to victory. By the Austrian campaign a few years later, every side understood the importance of artillery. The battle of borodino in 1812 was essentially a bloody stalemate as hundreds of cannon tore up each side, and borodino again paled in comparison to leipzig the next year.

The revolution saw the mobilization of the volunteer national guard. While the old armies of the monarchy were practically populated with beggars, the poorest of the poor under terrible conditions, being led by an aristocratic officer corps, many parts of the French army after 1789 were fighting for the idea of France (but only a small percentage of the army, as conscription still filled the ranks throughout the era, and the idea of France usually centered around Paris as opposed to say Marseille). Battles were more of a live action chess game, with agreed upon fields and considerable time for deployment. By the 1812 Russian campaign, all sides were mobilizing almost their entire populations. Millions of soldiers were in uniform and the destruction of the countryside was either encouraged or at least not considered an issue.

As I said originally though, I think the biggest under the radar influence was the theories of clauswitz (vom krieg) being taken to heart by the later commanders of Europe. Essentially you could reduce it down to the defensive side having the advantage, which you could see culminating in the massive buildup of defensive lines in ww1.

Sorry if there are typos in here as mobile doesn't recognize a lot of these names.