As it happens, though this seems little known now, the British & French DID push into the re-militarised Rhineland during the 'Phoney War' period of late '39-40. The incursion was actually quite small, & was, at the time, inflated out of all proportion in newspapers in Britain & presumably France.

There were also several small 'border incidents' on the static borders during the Winter of 39-40, which the Allies (because of being keen to be strongly defensive & hod the borders as best they could) usually got the better of, typically having superior numbers present. (Its notable also that the British - I don't know about the French, though it seems likely - were prepared with white cotton 'oversuits' for winter combat...whether these were official War Deparment issue, or if local commanders had them 'knocked-up' locally on their own initiative, I dont know. The Germans on the Russian Front werent issued with white snowsuits for winter until the winter of 1942, I believe).

Hmm...sorry to have gone off the pre-war topic of the thread