French politics were in turmoil in March 1938. Two days before Germany invaded Austria the entire French government had resigned. France was not in a position to oppose the invasion.
In March 1938, Britain was having its own political problems.
Anthony Eden, the Foreign Secretary, had resigned over Prime Minister Neville Chamberlain's decision to open negotiations with the Fascist dictator of Italy, Mussolini. With Chamberlain determined to appease Hitler, there was no political will to oppose Germany.
The British population were against the idea of another European war. The Anschluss (union) was not seen as a threat to Britain and, as both nations were German-speaking, there was a sense that there was no good reason why Austria and Germany shouldn't unify.
Anti-appeasers, such as Winston Churchill, were alarmed by Germany's annexation of Austria. They believed that if Hitler had a true claim to Austria, he should have used negotiation and diplomacy rather than force.