Randal Kolo Muani sent Didier Deschamps's side into a ninth-minute lead in Munich, but Lamine Yamal levelled the scores before Dani Olmo turned the match around for Spain.
France underwhelmed this summer, only winning one of their three group matches, before squeezing past Belgium in the round of 16 courtesy of a 1-0 success.
The Blues then needed penalties to overcome Portugal in the quarter-finals, but they were unable to navigate past Spain to secure a spot in the final against either England or Netherlands.
France's European Championship has now officially come to an end, as they will not be taking part in a third-place playoff at the competition in Germany.
When was the last third-place playoff at a European Championship?
There has not been a third-place playoff at a European Championship since 1980, with Czechoslovakia beating tournament hosts Italy 9-8 on penalties following a 1-1 draw.
According to FourFourTwo, UEFA decided to scrap the match due to poor television ratings and low crowds, so the fixture has not been held since Euro 1980.
England finished third at the 1968 competition, while Belgium and Netherlands were third in 1972 and 1976 respectively before Czechoslovakia triumphed in the one-off fixture in 1980.
The World Cup still has a third-place playoff, although it is a controversial fixture.
Croatia took on Morocco in the third-place fixture at the 2022 World Cup, recording a 2-1 victory, as the European nation finished behind Argentina and France in the tournament.
What now for France?
The future of head coach Deschamps is currently being called into question despite the fact that the legendary former midfielder has a contract with the Blues until the summer of 2026.
The 55-year-old was not prepared to discuss his position with the national side when questioned immediately after the narrow defeat to Spain on Tuesday night.
France's players will now have a short rest period before returning to their club teams to prepare for the 2024-25 campaign.
The Blues will then be back in action against Italy in the UEFA Nations League at the start of September, while they will also take on Belgium and Israel in Group 2 of League A.
Which team will Spain face in the final?
England and Netherlands will go head-to-head on Wednesday evening for the second spot in the final.
The Three Lions overcame Switzerland on penalties in the quarter-finals to book their position in the final four, while Netherlands recorded a 2-1 win over Turkey.
England have only won once in 90 minutes at this summer's European Championship, with Gareth Southgate's side struggling to impress throughout the tournament, while Netherlands have triumphed in three of their five matches and have not yet needed extra-time.