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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?

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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

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The short answer is no.

BIP 39 hashes the complete set of wallet BIP 39 words (typically in order specific sets of 12, 15, 18, 21, or 24 words). The complete set of BIP 39 words in different languages is documented at https://github.com/bitcoin/bips/blob/master/bip-0039/bip-0039-wordlists.md. Results of the BIP 39 related hashes shall differ radically if even if the list indices for different spoken languages match. This means internationalization interoperability between the BIP seed words between the different spoken languages supported by BIP 39 are impossible.

In other words, if you pick English stay with English BIP 39 seed words. If you pick French BIP 39 seed words, stick with French. Absolutely do not mix and match languages. Otherwise, the BIP 39 standard will be useless for restoring your funds in a HD wallets.

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