Given that the French had never had much issue about allying with the Ottomans to outflank the Hapsburgs... (and conversely the Hapsburgs cheerfully allied with the Persians to outflank the Ottomans...)
Realpolitik.
It incidentally occurs to me that this thread's title is quite possibly the first time ever I've seen the moniker "the Great" tagged onto ole Gustavus II Adolphus... which isn't really surprising, as his achievements weren't really those rulers generally earned the title with.
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