Born in France to a French mother and Togoese father, Boukpeti, 27, sought to compete for the west African nation when it became clear that he was too old to have a real shot of making the French team.
"Unfortunately, I've only ever been once to Togo, when I was very little, because my mother wanted to present me to my grandmother," said Boukpeti, who lives in Toulouse.
"But now I think I have a very good reason to go."
Rheinisch said he was "heartbroken" after missing out on a podium finish.
"One error is what cost me a medal, but I was really fortunate to come this far, he said.
"I can't complain, I've been riding my luck to get just through each heat to the final."
France's Lefevre went into the final as favourite, after Slovenia's Peter Kauzer had failed to qualify, but he struggled in the upper part of the course.
"I didn't have that little bit of excellence that I had earlier in the season," said Lefevre.
"I don't have any regrets, but I'm a bit disappointed because I was hoping to get France's first gold medal."
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