The Aussies also had the choice of the F-104 when they chose the Mirage - in fact , Lockheed's marketing was deemed to be so effective that everyone believed that the F-104 was a shoe-in, but the Mirage beat it.
There are some airbus aircraft purchased for Qantas, which have proven a bit of a disaster with turbine problems mostly.
Airbus are an airframer, not an engine manufacturer. Airbuses are good aircraft; I've worked on both 737s and A320s and both have their benefits and drawbacks. the thing is with European aircraft compared to US ones is that the Euros choose to do things slightly differently, but in some ways these differences are better that the US methond, although sometimes its the other way round. Airbus use standard American parts and also have stuck with imperial tooling, so any airline that has used Boeings for its fleet requirements and choose to change to Airbus can do so without the added expediture of staff re-equipping personal tooling.
One issue with European equipment is the supply train. Getting parts from the USA and US suppliers is cheaper and faster. I've also worked on ATRs, which are a different kettle of fish to other contemporary aircraft of their type. ATR prefers things to be done a particular way, which, like Airbus is distinctly European, but its supply train is far less reliable than using aircraft with a US supply base. ATR is different in that its parts are on the whole not interchangeable with US stock. ATR also like to have greater control over maintenance issues in terms of manuals, updates, repair drawings and all that stuff, which can be frustrating and time consuming, compared to North American manufacturers.
I would suspect, although I don't know, that dealing with Dassault might be like dealing with ATR compared with dealing with the likes of Boeing or Lockheed Martin. Not all Euro manufacturers are/were as frustrating, though. Although I've only done a small amount of work on the F-27, to my knowledge, Fokker were an easy firm to deal with. Also the kinds of problems that affect European military equipment are also prevalent in US manufacturers, as well.
Part of the problem the Aussie armed forces face is the demands the military staff place on the equipment and expectations - a manufacturer is of course going to endeavour to meet those demands. The Australian armed forces nominally ask for off-the-shelf, but want things to be built in Australia and modified to meet Australian needs. In some cases the Aussies have placed too much expectation on a piece of equipment - look at the Seasprite fiasco. Despite Kaman desperately attempting to produce the aircraft the Aussies wanted (the Aussie Seasprites were re-engineered old models with the work carried out by New Zealand contractors working for Kaman in Connecticut), it could not - partially because the expectations were too great. The Kiwis never had the same problem with their Seasprites as the Aussies did because they ordered off-the-shelf, whereas the Aussies did not. The British have ahd a similar problem with its Chinook upgrades, too.
In saying that, however, NHI are having issues with several countries and their new NH-90 helicopters - called the MRH-90 in Australia.