Are BIP39 mnemonics generated with a French list compatible with software that expects English words? BIP39 specifies different word lists in different languages. But I wonder if the word list generated by a software that gives me French words (e.g. Copay on iOS) can be used to re-create the same wallet using another software that expects English words.

I looked at the section From mnemonic to seed of the BIP39 specification.  Given that the mnemonic sentence itself is fed through the PBKDF2 function, rather than first looking up the indices of the words in the dictionary, I guess that the answer is no, and a French list can't be easily converted into an English list. Is this correct?

Doesn't this drastically reduce the interoperability of wallets using different word lists?  Specifically, how can I ensure that the word list I have for a wallet can be used in another software than the one it was generated with?
Given that the mnemonic sentence itself is fed through the PBKDF2 function, rather than first looking up the indices of the words in the dictionary, I guess that the answer is no, and a French list can't be easily converted into an English list. Is this correct?


That is correct. You can not convert a mnemonic generated using one wordlist to another since the mnemonic decodes to different byte arrays. For example the third English word is 3 bytes (able) while the third French word is 8 bytes (abdiquer). And consequently the seed (that you use in BIP32 functions) is going to be different.  


  Doesn't this drastically reduce the interoperability of wallets using different word lists? 


Usually when wallets implement BIP39 they implement all of it including all the wordlists that are linked in the protocol improvement. So they can remain compatible


  Specifically, how can I ensure that the word list I have for a wallet can be used in another software than the one it was generated with?


You have to check those wallets individually to see what they have done, either by checking their source code on GitHub or their website, or asking the community about for help. Lack of compatibility doesn't stop there.
Usually there is a page explaining it clearly. For instance Electrum uses an entirely different scheme although it still supports BIP39, or LND and wallets based on it use unique scheme called aezeed