Hi,
Caroubier Hippodrome was correctly tagged with leisure=sports_centre + sport=horse_racing. You have retagged it to leisure=horse_riding, but tag is not appropriate for hippodromes, compare OSM wiki:
https://wiki.openstreetmap.org/wiki/Tag:sport%3Dhorse_racing
https://wiki.openstreetmap.org/wiki/Tag:leisure%3Dhorse_riding

The French name of the preset for hippodromes in iD is "Course hippique".