France had been declining for centuries. In 1700, many(if not most) would have declared France the strongest nation in Europe(strongest army and most populous).
France was easily the most powerful country in Europe up until the end of the Napoleonic Wars, and even then, it took all of Europe to beat them.
Also, until the formation of Germany, they were still the most populous country in Europe, and their army was still amongst the best, sadly it has perpetually suffered because of poor leadership (at least in the XIXth century and beyond).
By 1900 they had a smaller industrial base then America, Britain and Germany. They had a weaker army then Germany, and weren't far ahead of Russia or Austria-Hungary. By the outbreak of WWI, they had a smaller population then Germany, Austria-Hungary, Russia, or the United States.
These comparisons are 1) Unfair and 2) Unbalanced. Germany, America and Britain are the undisputed superpowers of the time, and no one held a candle to them. This of course doesn't take into account the fact that, socially, France is very different from those country, and has been for most of its history a very rural and traditionalist country. There might also be something to the idea that Catholic Countries have more trouble industrializing or modernizing (it can't be just coincidence that the three industrial powerhouses of the time were vastly protestant).
As for the population, Austria-Hungary ruled a vast, multicultural empire with little to no cultural cohesion across the Empire, Germany was a recently unified country which, and this applies to Russia as well, held considerably more territory than France. Also, Russia's population was nowhere near as well off as any of the other European countries.
You also have to keep in mind that, demographically, France is an anomaly, since they seem to have transitioned into a far more modern demographic structure much, much earlier than any of its neighbors, so while all of its neighbors were experience the industry-fueled population explosion, France had already seen its population growth pretty much stabilize.
By 2000, France went from having a gigantic oversea's empire to next to nothing, a weaker economy then they previously had(relative to the rest of the world), a military that many could say(possibly wrongly, but this isn't the point of the topic) wasn't top 5 in the world, and a small shrinking population.
By 2000, every single country that ever had an overseas empire has been reduced to, essentially, nothing, this also applies for Spain, the UK, Germany, Portugal... you get my drift. This, of course, does not take into account that France still has sizable overseas possessions, and if I'm not mistaken, actually has the largest exclusive economic zone in the world, thanks to all the tiny islets they have.
Also, their economy may be weaker than it was before, but that is more as a result of a worldwide growth in regions that traditionally weren't really wealthy, such as East Asia and Latin America, and as a result,
every country's relative wealth has "shrunk". And despite that, I would still not call France's economy much weaker than any of its neighbors, since they all suffer very similar problems.
As for the retarded notion that France's military is anything but top notch, seriously, people at AH.com should honestly know better. The walkover that was WW2 was an aberration, that even the Germans weren't expecting, and was more a result of poor strategic planning and its upper echelons being firmly rooted to WW1 strategies than anything else. Today, France has an army that is just as good as any of its neighbors, including one of the top air forces in the world.
Also, considering that the only two countries that could actually be better than France militarily are the UK and the US, I fail to see how it's at all possible that France isn't amongst the top 5 armies in the world. Really, who could have a better army? Russia?
Oh, and France's population isn't small, considering it's currently just over 60 million, and it's also
not shrinking, one of the few populations in Europe that's actually growing naturally. There's going to be a generational "gap" caused by the baby boomers retiring, but after that things should stabilize for France and its population will continue to grow (it's fertility rate is somewhere around 2.0 and 2.1, which is the ideal number for natural growth).
With a POD of 1900, what's the best case for France? What is the largest, strongest, and most influentional they could be?
Really, avoiding both world wars, or at least not suffering such huge damages (France's industrial capacity was reduced by over 40% compared to what it was in 1939 after WW2), especially population wise, would do a lot to improve France's current situation.
Maybe a more organized decolonization results in a Francophonie which is a lot more similar to the Commonwealth, but considering that 1) the Francophonie has so little in common with the Commonwealth and that 2) so many of France's ex-colonies are still pegged to France's currency, as well as France conducting military operations independant of both NATO and the UN in several former colonies (Sénégal, Côte d'Ivoire, etc.), I daresay that France is still a pretty influential and strong nation.
Also keep in mind that France, along with Germany, essentially dominates the EU, and they did after all help found one of the most important modern organizations (EU).
As for strength, in terms of relative strengh, I'm almost certain that France is probably the most powerful country on the continent (excluding Russia and the UK).
France is also a technological leader in Europe, and they depend far less on oil than most other countries do, since they have over 50% of their energy derived from Nuclear power.
I don't think france could actually get much bigger, unless they take the Saarland from Germany after one of the two world wars, and possibly take some territory from Italy as well.