Are EU treaties agreed between member states or between member states and the EU?
Is the EU a sovereign entity in and of itself?
You can read the treaties yourself.
For example in the Maastricht Treaty, the treaty is between the "High Contracting Parties", that is the countries themselves. The parties are actually listed as the heads of state of the various countries, and are countersigned by the relevant ministers. For example, the UK's entry:
HER MAJESTY THE QUEEN OF THE UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND:
The Rt. Hon. Douglas HURD, Secretary of State for Foreign and Commonwealth Affairs;
The Hon. Francis MAUDE, Financial Secretary to the Treasury