First, Airbus was originally organized by French nationals, under French law, using a legal structure with no US equivalent. To say that Airbus is not a French creation is to fail to give credit where credit is due.
Second, the 747 was not funded by the US government in any way. Boeing did do a proposal for a large transport, as did Douglas. Both lost to Lockheed, which went on to win (lose?) the contract and build the C5A. Also, the commercial 707 bears little resemblance to the KC 135, and was not built on the same tooling. A classic Airbus argument is that Boeing has received the benefit of decades of government subsidy. I suppose that our government should have opened, say, the B-47 or B-52 contract to European bidding. Air Force One should probably have been a Caravelle, a DH Comet, or maybe, later, a Mercure. To say that Boeing somehow triumphed based upon government contracts is absurd. If defense business can support a company's commercial side, then where are all of the Martin, Northrup, Convair and Lockheed jetliners? Defense business didn't seem to help De Havilland all that much and when a famous French builder of high performance fighters tried its hand in the airliner business, the results were not impressive, although they do build some great business jets.
Third, of course Airbus buys American components. It is far cheaper to buy proven pieces off the shelf than it is to design them from scratch. Airbus thus shows good business sense. In the same way, if Boeing can find Asian risk sharing partners, it follows that Boeing will look to Asia.