The main cause of France's relative decline compared to the other European powers was her sluggish population growth. France, Germany, and the UK (Modern French borders, Kaiserreich without Alsace-Lorraine, and entirety of the British Isles), their populations are 30.5 million, 24.3 million, and about 19 milliion, respectively in 1815. By 1913 (using the same borders as listed above) this had evolved to 41.5 for France, 65 million for Germany, and 46 million for the UK (+36%, +167%, +142%, respectively).
In terms of productivity per capita France did relatively ok. Using 1990 dollars and the Maddison project:
https://www.rug.nl/ggdc/historicaldevelopment/maddison/releases/maddison-project-database-2013
France: $1135 (1820) -> $3485 (1913) (+207%)
U.K.: $2074 (1820) -> $4921 (1913) (+137%)
Germany: No data in 1820, but probably similar or a bit less than France -> $3684 (1913)
So in terms of productivity/prosperity per inhabitant France didn't really lose that much relative ground in the 19th century, though I'm sure France could have done better. The main thing France needed to have to conserve her status as a first rank power, is to have a greater population. France's low 19th century birth rate is still not fully understood, but most sources I've read suggest that the Revolution was at least part of the reason (
http://people.qc.cuny.edu/Faculty/Neil.Cummins/Documents/France TSA MAY_2011_BODY.pdf). So by the fall of Napoléon French demographic dominance is, I feel, pretty much bound to decline at this point, but maybe the decline in birth rates can be slowed down. Just spitballing here, but maybe a more stable regime led by a moderate-conservative Catholic Bourbon that slowly transitions into a constitutional monarchy would help France's demographic/demographic development, instead of the constant instability and regime changes. So I think avoiding the regime of Charles X is going to be pretty necessary, or maybe having him die earlier, but beyond that I'm not sure what would be the right regime to lead France.