Except that "US companies" incorporated in Ireland aren't US companies. Can't European companies also incorporate in Ireland?
A company whose primary employees are in Europe and whose primary customers are in Europe can still be incorporated in Delaware and traded on the NYSE. These tax avoidance mechanisms aren't for "US companies," they only work if you're in practice an international company. A "European company" which is also in practice an international company could do the same by becoming nominally a "US company" without changing anything of consequence about their operations. Because international companies don't really care where they're incorporated.
The trade war isn't between US companies and European companies, it's between companies big enough to be "international" and everybody else.
While I'm sure it can be minimized, the US doesn't have a particularly low corporate income tax rate.
> And if they paid that tax in the US [...] how would that help Spain and France?
Companies like Google not having to pay tax on revenues outside the US is essentially a government subsidy. One that creates a "slush fund" for US companies to acquire their European competition. We're essentially in a trade war, just that Europe hasn't realized it.