The french Second Empire was not "significantly weaker" than the rest of Europe. First of all "weaker" is far too vague, and can means about anything from military power to the level of industrialization or the economy of a country. Moreover, the Second Empire didn't lose three wars against Germany, but only one, the Franco-Prussian war in 1870. It was also that defeat that put an end to the Second Empire.

On the military side, it can't really be said that the Second Empire was weak. While it's true the Franco-Prussian war was a complete defeat, the few other wars and military operations led by Napelon III before were mostly successful (like the Crimean War or the Second Italian War of Independance). There are a lot of things to consider about the 1870 defeat. Firstly both France and Prussia wanted this war, so both of them tried to get a casus belli. The goal was to not be seen as the provocator in this situation, in order to get allies (France counted on the help of Italy and Austria-Hungary, while Prussia wanted to unify all the german countries under its direction). In the end, it was France which declared war on Prussia, but its casus belli didn't convince the other countries, which made it lose its potentiel allies, while most of German countries rallied to Prussia. So in the end there was a huge gap in the number of men both side could mobilize (300.000 in France against 500.000 for Prussia and its allies at the beginning of the war). The second factor which seems to be determinant was the fact that, due to their recent wars, Prussian was far more experienced in modern war than France. An example of that is the use of train to bring soldier to the border. Both country had comparable railway network, but Prussia had the occasion to try this new logistic tool in its previous war against Austria, and there mobilization was thus far quicker than in France, which was determinant in the quick resolution of this war. France in general wasn't really prepared for a war of this scale. But still, it must be somehow nuanced. It's a common belief that German army was one of the best in Europe in the modern age, and particularly better than the French one during the Franco-Prussian war or the World War I. But this is often quite misleading. For example, French soldiers had actually better rifles than German in 1870. Since both country used a conscription army, the soldiers themselves weren't really different. German soldier isn't better than French soldier. In this war, it was mostly because of the previous war Prussia fought that its army (and not its soldiers) was better prepared.

On the industry side, France had to deal with quite a lot of crisis along the first half of the 19th century, both economic and political, which delayed the industrial revolution because of global instability and the lack of funds. But at the end of the Second Empire, France had caught up to the industry of Britain and Germany, even if it was still behind. It experienced a huge annual industrial growth rate between 1850 and 1870, around 2~3%, and quickly modernized. So it wasn't as industrialized as England or Germany, but it was still one of the most modernized country. I'm not sure if it was ahead or behind Russia tho.

Sources for all this are french ones, “Dictionnaire du Second Empire” under the direction of Jean Tullard, (to be more precise the following articles of this book : Guerre de 1870 and Industrie), and some videos from the French youtuber Sur le Champ, who makes videos about the history of war (I'm talking especially about the ones on the transition from Napeleon wars to modern war and the World War I).