That’s just not the case at all. The US under the Articles of Confederation, yes, but not the US under the Constitution.
• The EU does not have the power to tax the citizens of the EU directly; neither did the US under the Articles of Confederation. Both are/were dependent on the member states to provide financing. The federal government under the Constitution does have the power of taxation directly, without needing to rely on the states for funding.
• Although it’s a bit complicated, the general rule is that EU laws don’t apply directly to citizens of EU states; they need to be implemented by the individual nations. Congress under the US Constitution has the power to impose its laws directly.
• The EU and the US under the Articles of Confederation do/did not have an executive branch which could implement its laws directly; both are/were dependent on the member states to implement laws.
• The EU and the US under the Articles of Confederation don’t/didn’t have courts at first instance that the citizen could go to. There are upper level courts in the EU, but they are mainly for disputes between the member states and the EU government, with only a limited ability for citizens to be a litigant. The US under the Articles of Confederation didn’t have courts at all. The US under the Constitution has its own judicial power, a Supreme Court, and inferior courts established by Congress.
• The EU and the US under the Articles of Confederation were both established by treaties between the states. The US Constitution was established by the citizens of each state, in conventions, not by the states themselves.
• Since the EU is established by international treaties, each member state retains the full power to leave the EU unilaterally (Article 50 of the Traty of Lisbon, 2009). A departure can be messy and there is an incentive to reach a deal to make the exit as easy as possible, but ultimately, if a member of the EU wants to leave, it has the unilateral right to do so, recognized by the other members of the EU. The proof that a state under the US Constitution has no such unilateral right is left as an exercise to the reader.
The nature of the US Constitution, as a treaty established by the states, or as a supreme law established by the people, was one of the major theoretical disputes between Madison and Patrick Henry in the Virginia ratifying convention for the US Constitution.
Madison was clear that the Constitution was not a treaty, and that’s why he had pushed hard at the Philadelphia Convention for popularly elected ratifying conventions, rather than ratifications by the states. He argued that ratification by the states would make the Constitution a treaty, which each state could ignore as it saw fit. Ratification by popular elections in each state made it a supreme law, created but the people directly, not through their state governments.
Henry agreed with that theoretical analysis, which is precisely why he opposed ratification. He argued that the state delegates at Philadelphia had no right to draft a Constitution that began “We the People…” They only had the power to bind their states, and the Constitution should be considered a treaty between the states. The attempt to make it a popular instrument, rather than a state treaty, was repugnant to him. He saw that the proposed Constitution would create “a more perfect union”, which he disagreed with.
So no, the US government under the Constitution is not closer to the EU model than to a national model like France. France is a unitary state, true, and the US is a federal state, but the federal government has powers and roles that the EU simply does not have. The federal government also has a constitutional status, which the EU, the creation of international treaties, does not have.