I have added the new field in Customer navigation section near the
Sign In, For that new field I need to fr_FR translation where I need to add the translation text? Those translation files are working from which file please tell me.
have you used this syntax where you put your text?
<?php /* @escapeNotVerified */ echo __('Your text') ?>
data-bind="i18n: 'Your text'"
You can installed French Language pack
Or you can Create language file at below path and add translation text. app/design/frontend/Vendor/theme/i18n/fr_FR.csv
Not tested: But You can try using
/vendor/magento/module-customer/i18n directory and check the translation.
Hope that may help you.