The House of Valois doesn't die out: could Navarre remain independent?

Just something I was wondering about. IOTL, when the Valois died out and Henry of Navarre became the French king, the rump Navarrese kingdom that survived the Spanish invasion during the early XVI century was incorporated into France. Now, if Charles IX or Henry III had sons, denying any possibility for the Bourbons receive the French throne, could Navarre have survived as an independent kingdom, or were they too weak that would be conquered by France soon or later?
 
my opinion...it would be incorporated into france the same way spain took lower navarre. if it had a coast or at least a port it might have more of a chance, but somewhere down the line france is going to take it
 
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