POSSIBLY. While you are resident in France and comply with the conditions set by the national employment authorities, you remain entitled to unemployment benefits.
If you decide to follow vocational training in another EU country, under certain conditions you might be entitled to continue receiving unemployment benefits for a limited period of time.
The authorities can't refuse to continue paying your unemployment benefits for the sole reason that the training takes place in another EU country. But they can refuse if the training scheme does not meet any specific criteria that exist under French law.
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