Take a bus to Calais Ville station. The bus service operates between 1000 and 2000. The fare is �1.50 or �1.
Take a train from Calais Ville to Dunkerque. The direct trains are very infrequent. They take just under an hour, with a fare of about �7. If there's no direct train available (and you don't want to wait) you might have to travel via Hazebrouck. The total journey time on this route is roughly between 1� hours and 2 hours, depending upon the connection. The fare varies between about �10.50 and �13.50.
http://www.raileurope.co.uk
From there, you can get a bus to De Panne. Some web sources refer to service 1A, others refer to number 2B, so you might have to make enquiries in Dunkerque. However, the Thomas Cook Rail Map of Europe shows that there's definitely a bus link between the two towns, so you shouldn't be stranded.
Chris