Asian shares declined Thursday and U.S. futures turned higher after the S&P 500 slid 3.5% overnight for its biggest drop since June.

The selling in U.S. markets followed broad declines in Europe, where the French president announced tough measures to slow the virus' spread and German officials agreed to impose a four-week partial lockdown.

So far, the measures are not as stringent as shutdown orders that swept the world early this year, but the worry is they could still hit the already weakened global economy.

In Asia, some countries appear to be keeping the pandemic in check, while caseloads...