(1) Replace US president with a Commission of Presidents. One from each state (well, EU only has 27 member states). Each Commissioner is appointed by state legislature, not elected. No more presidential elections. This is the EU Commission.

(2) Replace US senate with a meeting of secretaries, or heads of departments from each state. Only one relevant representative from each state. But the senate composition is not fixed. When the senate discusses e.g. agricultural policy, each state sends their secretary of agriculture, of head of their department of agriculture. No more senate elections. This is the EU Council of Ministers (a.k.a. Council of the European Union or just "The Council").

(3) The house is the EU Parliament.

Take the right of legislative initiative away from the congress, and give it to the Commission of Presidents. The Commission writes the bills, and the senate and the house can only approve or disapprove (with comments).

(4) Change the states to follow the European model: The governor is not elected, but appointed by the state legislature, and is called "prime minister". (Except France has a presidential model.)

(5) The president / Commission is like a CEO. To supervise the CEO, we need a board. The heads of states (governors) meet 4 times per year to discuss and set broad and long term goals. This is the European Council.