The answer is a broad Yes, but you could argue why it's Yes for days. I'm going to answer from the perspective of Economic History, and draw some connections between economic base and the capacity to act by a state (or a monarch, as it would be more correct to specify in this case).

While prestige is difficult to quantify, you can nonetheless look at stand-in metrics to get a gist of a polity's standing and capacity to act in the international pecking order. I like to use Angus Maddison's rankings of historic per-capita GDP levels. Maddison set up a research project at the University of Groningen that's outlived him, and does a good job of approximating what the average worker's wealth probably would have been in different parts of the world at various historic times. This is a useful tool to assess how much wealth a monarch could tax and ordinary people could spend on projects contributing to various definitions of "prestige." There are however non-quantifiable caveats that mitigate the usefulness of GDP as a stand-in for state capacity, the clearest being the kind of government system in place and its capacity to extract resources (this was the case in Italy, where high economic development contributed to the accumulation of cultural prestige in form of advancement of the arts and sciences while political fragmentation, conflicts, and organizational immaturity meant that the actual capacity and prestige of the Italian States was close to zero; you could say that while individual Italians had achieved leadership and prestige various fields, their governments did not). Some might also take issue with the accuracy of any process of quantifying wealth levels through history, but literature in economic history published in the past fifteen years is generally consistent with Maddison's methodology and findings.

Now, it's also worth saying that in many places resources to estimate these numbers simply don't exist or only exist in rough and sporadic estimates. Perhaps surprisingly, France is one of those places. Maddison doesn't feel comfortable coming up with estimates for France between the Roman Empire and the third decade of the 19th century. Only after the Napoleonic bureaucratic apparatus sets up a sensible system of taxation does the job get easier. The fundamental problem with assessing France has to do with the way pre-industrial (or rather pre-revolutionary) french society was structured. It is unsurprising that data on wages for construction workers are easy to come by in the 1380-1540 period, where the French Monarchy was definitively reeling in the aristocracy. Further, the bulk of data comes from Normandy, Alsace and Île-de-France. Indeed, some 40% of observations come from the Paris basin and surrounding Île-de-France! The situation doesn't get much easier as time goes on, as even the "Official Inquiries" carried out in the 17th century make the fundamental mistake of surveying prices and not wages (ideally you would need both to assess standard of living and prosperity, however in this pre-globalization era produce is necessarily highly regional and seasonal, making it a questionable metric for normalization). So how can we know much much prosperity the French monarchy could tap into in order to project power, commission artistic and architectural works, and undertake other projects that would contribute to notions of prestige?

Some earlier studies do exist that look at economic output in specific regions of France (Baehrel in 1961 and Le Roy Ladurie in 1966) while others limit themselves to the immediate pre-industrial era (like Toutain in 1961 and again in 1987). But the only study that I know of that really tackles the whole of France is Ridolfi's in 2016. Ridolfi finds that the whole, real wages in France did not really grow between the second half of 1300 and the end of the 18th century. This stands in stark contrast with England and the broader North Sea economy, where wages steadily increased starting in precisely the 16th century. So was France stagnant while England was on the rise? Probably. But the argument has a lot of nuance.

What is certain is that economic development in England took a very different shape. Unlike France and other Mediterranean-facing economies, the British Isles are agriculturally unproductive and labor-scarce. In a world where agriculture is the main economic activity, until the Great Divergence in Europe (for that is how Robert C. Allan at Oxford has called the process that starts in the 16th century) England trails the rest of Europe in overall economic development and cannot even support a large population. So England is less prosperous and less populous than France, meaning the English state had less capacity to act, the Hundred Years War was a Fluke, and we have an answer. Or do we? There is an enormous caveat: labor scarcity makes labor more expensive. Allan finds that in 1500 a building craftsman in Paris earned 4.4 grams of silver per day, while his counterpart in London earned 5. In 50 years, a craftsman in London would earn 6.9, a hundred years after that 14.5, and by the cusp of industrialization 28.9! One of the greatest strengths of the French state would be the enormous labor pool which allowed French armies to find fresh recruits to fuel two centuries of near-continuous warfare, but abundant population would also depress wages. There was less taxable income in France, and this decreased the overall ability for the state to project. But again, this isn't the end of the story: an ongoing debate in the field of economic history looks at the impact of demographic factors as opposed to institutional factors, and institutional factors in England (notably the body of law around taxation and parliament) worked to the detriment of the monarchy and worked to create a lot of mobility between the lower rungs of the landowning aristocracy and the entrepreneurial urban middle class (especially in London).

Mind you, overall wages in Paris did rise after all: Parisian wages surpass London wages midway through the century, but by the century's close London wages were back on top. And besides, Paris was both the capital of a colonial power and located on the edge of the North Sea economy growing faster than the rest of Europe. Our thesis of a stagnant France holds taking a stand-ins for other places in the country (Allen doesn't look at other French cities) just look at wages in Strasbourg, not without significant jumps and dips, they seem to hover around 5 grams of silver per day for three centuries. While I'm looking at skilled laborers, wages are lower and even more stagnant for unskilled workers. You can read the whole article here

Ridolfi corroborates this, noting that as early as the 15th century workers in England were supplying more labor than would be required to maintain subsistence. This is not only a signal of labor scarcity, but also implies that disposable income could be accumulated and with it economic growth. France instead was fundamentally locked in what Ridolfi calls a growth-less economic system. So any prestige-building expenditures had to be driven by the aristocracy or the monarchy. So in the 16th century, was France more agriculturally productive? Yes. Did France have a larger manpower pool? Yes. Was France involved in more European conflicts? Yes. Were workers better off in France? Probably not. Which state is the more prestigious? Probably France, but it all depends on what your metric is.

Was England on the European periphery until the Great Divergence in Europe? I guess you can answer Yes to that too. But over the course of the 16th century, did your prosperous London merchant have more means to accumulate disposable income to spend on art, luxurious foreign foods like parmesan cheese, and renovations on his country home and/or townhouse? The answer is Yes, and that level of prestige and prosperity would be more difficult for his social peer in France to achieve. On the other hand, the French Monarch would have greater capacity to act than his English counterpart, because even though per capita taxable income was lower, he had more purses to tax and soldiers to recruit in absolute.