According to this dictionary of insurance terminology, an "assurance en première ligne" translates as "prime" or "primary insurance". See:

"Assurance en première ligne (Prime Insurance ou Primary Insurance) Assurance qui paye en premier par opposition à « assurance complémentaire » qui paye seulement après que la limite de l’assurance en première ligne a été atteinte."
http://www.aon.ca/francais/ars/insterms/

The same definition appears on another site in English:

"Prime Insurance or Primary Insurance
(Assurance en première ligne)
First paying insurance coverage as distinct from "Excess Insurance" which pays only after the prime or primary insurance limit is exhausted."
http://brownbrosinsurance.com/glossary_p_q.html

Lots of hits in English for 'primary insurance policy', which pays out before any other supplementary or sub-prime policies.

Hope this helps.