There are two names for the country CZ (the corresponding geoname id is 3077311) in the iso Language FR (see the alternateName.txt file):
Furthermore, "Tchéquie" is preferred to "République tchèque" in geonames API (see the isPreferredName column in the alternateName.txt file)
However in other languages, it is the contrary: see Spanish where Republica Checa is preferred to Chequia, or English where Czech Republic is prefrred to Czechia.
Why using Tchéquie and not République tchèque in French then?
Wikipedia does not say anything about a specificity to French language regarding this case.