Rt Revd Patrick Lynch's comments come just days after he praised the Home Secretary Theresa May and the French Interior Minister Bernard Cazeneuve for what he called their "commitment" to helping genuine asylum seekers.
They also come on the day Eurotunnel operators threatened to sue the government for 200 million pounds if the route is closed overnight, because of the loss money it will incur.
The threat of legal action comes after reports government ministers discussed potentially shutting it down after dark to avoid further security breaches.
This has raised concern, given that the government recently spent £7m to increase security at Calais.
Bishop Lynch has also praised the work of French churches and others in helping migrants, and urged governments and NGOs to solve the root causes of the migrants crisis, namely the various reasons they are leaving in the first place.
Many Christian migrants are fleeing persecution from Islamic State and other extremist groups, while other refugees are fleeing war or other forms of persecution, or seeking better economic opportunities.
He said: "I am deeply concerned over the deepening humanitarian crisis involving thousands of migrants unfolding in Calais. The crisis has developed over a decade and challenges us all, both as Christians and as Europeans.
"First, in solidarity with the most vulnerable migrants we recognise the local pastoral, humanitarian, and compassionate response from the French Church and call on the French authorities to redouble their efforts in providing adequate reception facilities for migrants... The Catholic Bishops' Conference of England and Wales will be making a material contribution to those efforts.
"We must examine as a matter of urgency the arms trade that fuels armed conflict and civil war, climate change, unjust economic policies, poverty and corruption as some of the underlying causes of this fundamental global trend.
"The safety of vulnerable women and children who may fall prey to smugglers and human traffickers is paramount and must be addressed."