Married in Taiwan, Spouse doesn't want to register marriage in home country (France)

Of course you didn’t. Would help to say as to why. This requirement was waved in your case. Your situation does not apply to other countries. e.g. France in this case

As of January 1, 2014, he British government no longer offers the service to register marriages that take place abroad.
Marriage certificate registry service discontinued for overseas Brits - GOV.UK

In USA one also can’t register one, since a register does not exist.

It is a strictly enforced requirement. One need to show the registration or that it is not possible.

Then tell BOCA their website is wrong. And help people like @Fuzzy_Barbecue to get spouse resident visa without registering Taiwanese marriage abroad A foreigner’s experience in 2018 trying to get residence visa for a Filipina Wife


Original and one photocopy of marriage registration issued by competent authorities of the applicant’s country.

Bureau of Consular Affairs, Ministry of Foreign Affairs, Republic of China(Taiwan)-Resident Visas for Foreign Spouses of R.O.C.(Taiwan) Citizens Having Household Registration


If one party is a Foreign National, file for marriage registration first at your respective embassy or consulate, for information on the consular district designated by the Bureau of Consular Affairs of R.O.C.(Taiwan) , please visit 外交部領事事務局全球資訊網

https://www.roc-taiwan.org/ph_en/post/683.html