8,440.

This is coolbert:

Look before you leap!

Here from the book "TOP SECRET ULTRA"  by Calvocoressi we have that exact amount of German encrypted radio traffic as secured by the Enigma machine as read in that time prior to and during the Battle of France [1940]:

"work on Enigma went on separately at BP [Bletchley Park] and Vignolles [PC Bruno]. There was some collaboration. Each outfit agreed to given the other any Enigma daily settings which might be unravelled. Vignolles was forced to shut up shop on 23 June, 1940. By then the Franco-Polish team had broken 110 Enigma settings often with considerable delays: a key for 26 October, for example, was broken on 17 January. In all Vignolles read 8,440 German messages. Rather more than 1,000 of these related to the Norwegian campaign., some 5,000 to the campaigns in France. During these months 83 per cent of all Enigma breaks were made at BP. The first was made in Vignolles in January 1940 on the basis of work done at BP."

That amount of messages "read" by the allies during the Battle of France [1940] considerably more than what I had expected.

BUT what messages de-crypted and presented to the senior commander either not [?] in real time or that commander not having action-able intelligence presented to him in a fashion allowing him to make informed and correct decisions.

It would seem that Enigma de-crypts were available during that Battle of France [1940], the use however seems to have been scant to negligible

coolbert.