Ok, you obviously have tested this for these specific pairs (EURUSD-EuroFX vs S&P500-ES), but in general I would think there is no great correleation between currencies and stock markets. You don't mention a timeframe on this, but looking at big timeframes with ⬠at around 1.29 at years end .. and then the slump in both S&P and ⬠and now towards the end of the year a return to levels close by .. perhaps.
I do know the european investors see buying opportunities in US markets when the USD gets cheap, and of course the currency offsets are important in investing in foreign markets. Uhh, and not to forget hedgers, of course.
Also for today and next week's reminders:
[14:42 EUR/JPY: Massive EUR Debt Redemptions Could Weigh On Cross] San Francisco, Oct. 22nd: EUR/JPY is at 136.72 and continues to only show marginal change through the morning. The cross, though stable over the last few sessions, is at risk of heavy selling pressure next week due to large Eurozone debt redemptions coupled with large coupon payments. Redemptions close to EUR22 bln are tipped along with coupon payments topping EUR15 bln. Only EUYR5 bln in new issuance is tipped to absorb these flows. Japanese investors, growing wary of poor economic data from the Eurozone, and looking at multi-year low yield spreads against JGBs, may choose to cash in their chips, so to speak, and take profit on the hefty FX gains seen on this cross since 2000. This increases the risk of a push through 135.00 next week, particularly with USD/JPY still remaining heavy.
edit: the action already seems winding down for the last 30-40 mins ...

OTOH, that could just be the push upwards being foiled.