What does "FRANCE TO PLACE" mean?

From Pat Hobby, Putative Father by F. Scott Fitzgerald:

He searched the orange pages frantically. Below the form sheets, the past performances, the endless oracles for endless racetracks, his eye was caught by a one-inch item:

LONDON. SEPTEMBER 3RD. ON THIS MORNING'S DECLARATION BY CHAMBERLAIN, DOUGIE CABLES 'ENGLAND TO WIN. FRANCE TO PLACE. RUSSIA TO SHOW'.

Clearly this is a shorthand for something, but what?

It's a betting term. Win — first place. Place — second or first place. Show — third, second or first place.

Source: oddsshark.com (among others).

Suggesting England would "win," France would finish second and Russia third. That is, someone was setting odds on the outcome of the war.

horse racing term

to place TFD

Games Second position for betting purposes, as in a horserace.

The prediction of the race is for England to win ... Russia to come in 3rd. But without more context ( doubtful horses name's could be England, France and Russia) it could be a political or some such metaphor.

Below the form sheets, the past performances, the endless oracles for endless racetracks

The context is a newspaper for horse racing bettors.

LONDON. SEPTEMBER 3RD. ON THIS MORNING'S DECLARATION BY CHAMBERLAIN

On September 1st, Germany invaded Poland. As a result, on September 3rd 1939 British Prime Minister Chamberlain declared war on Germany.

See https://www.youtube.com/watch?v=rtJ_zbz1NyY

DOUGIE CABLES 'ENGLAND TO WIN. FRANCE TO PLACE. RUSSIA TO SHOW'.

As others have noted, this is horse race betting parlance for England will win, France will come in second, Russia will come in third.