I don't think so: most of that period was French cultural and military dominance, especially when "the Age of Louis XIV" kicked in. There were, of course, ups and downs but the Hapsburgs never reached the same level of influence as Louis XIV did.
I think part of Austria's claim to fame here is that on paper, France should have rolled over Europe from the end of the 100 Years' War onwards due to their disproportionate demographics, wealth, and productivity but never managed to successfully leverage it till Napoleon came along. Austria gets major props for being the David to France's Goliath for 3+ centuries straight.