How silly can they get? France was a modern country and it is ludicrous to assume they would compromise security to such an extent to have their armed forces using civilian lines.
I can see it in an emergency, if the military hasn't had time to rig its own secure wire network. It's not as silly as it seems to us in the 21st century, but most calls were switched through human operators at exchanges and in trunk lines. William Shirer, in his Paris Diary, notes the problems CBS had in arranging telephone calls for William Murrow in London and the correspondents in Berne and Rome. The French network was overtaxed, and neutral broadcasters could wait for the official communique from HQG: "Nous avons gagné."
This was not only a French problem, but plagued all the warring powers during the War. They haven't yet released the archives from Paris but some of the British confidential dispatches were released in 2009. How much do you send over the air, with the possibility that your messages have been heard and deciphered by the enemy? On the other hand, if you're moving fast, you don't have time to lay wires. In the initial phases of the German attack, civilian phone lines could be commandeered by the Republic, and, IIRC, were in the Ardennes.