Short answers, pulled from the story.
The remilitarisation of the Rhineland began on the 7th of March 1936, when nineteen German infantry battalions entered the demilitarised zone. The operation directly violated Articles 42 and 43 of the Treaty of Versailles and Articles 1 and 2 of the Locarno Treaties.
General Maurice Gamelin warned the French government that any challenge would require full national mobilisation, costing thirty million francs per day and risking a full-scale war. France was simultaneously facing a severe financial crisis, and its intelligence service overestimated German troop strength in the Rhineland. Only Czechoslovakia among France's eastern allies was firmly committed to joining such a war.
Germany violated Articles 42 and 43 of the 1919 Treaty of Versailles and Articles 1 and 2 of the 1925 Locarno Treaties. Both instruments forbade Germany from stationing military forces in the Rhineland region. The Locarno violation was considered especially significant because Germany had accepted those terms voluntarily.
Hitler used France's ratification of the Franco-Soviet Treaty of Mutual Assistance as his stated justification. Foreign minister Baron Konstantin von Neurath argued that this bilateral arrangement violated the spirit of the Locarno Treaties and posed a threat to Germany, giving Germany grounds to renounce Locarno.
Neither France, Britain, nor the League of Nations imposed sanctions or military consequences on Germany. At the League of Nations Council, only Maxim Litvinov of the Soviet Union advocated sanctions. Ambassadors from thirteen nations, including Sweden, Poland, Norway, and Finland, declared any such measures economic suicide for their countries.
The remilitarisation allowed Germany to begin constructing the Siegfried Line, removing France's ability to threaten a retaliatory offensive in defence of its Eastern European allies. Belgium renounced its defensive alliance with France by October 1936, and both Czechoslovakia and Romania seriously considered abandoning French alignment entirely.