Since the UK left the EU, a new safety regime for the Channel Tunnel is yet to be agreed.
France says governance of the entire tunnel, both the French side and the British side, should be under French control with the European Court of Justice settling disputes.
However, MPs on the House of Commons European Scrutiny Committee say that would be a 'power grab'.
Sir William Cash MP, Chair, European Scrutiny Committee said: "We're confident... these things can be handled and managed and these are the right people to deal with it. That's the key issue, and it's not actually anything more than good cooperation and good understanding between the mutual participants."
Since it opened in 1994, there have been three major fires in the Channel Tunnel - in 1996, 2008 and 2015.
Both French and UK governments have spent tens of millions of pounds on security after repeated attempts from migrants to walk through from France to England.
There has also been power failures, stranded passengers and serious security breaches, spanning many years, by migrants clambering onto trains to make it into Kent.
Sir William Cash is also among those concerned, that French control of governance and key decision-making could lead to UK companies being frozen out of future investments in rolling stock and CT infrastructure.
Get Link, formerly Eurotunnel, said: "This is a technical negotiation. Clearly the CT has remained open. We are confident the two governments will reach an agreement."