Some native keyboard accent shortcuts not working since OS X 10.11.3 Update

Solution 1:

The standard US keyboard layout always yields a § if alt6 is pressed.

To get your desired results enable the US extended (or ABC Extended in OS X 10.11) keyboard layout:

• alt6 -> ˆ
• alt6+e -> ê
• altc+c -> ç

Solution 2:

Go to system preferences/keyboard/input sources and make sure that only the item called "US International PC" is on the list, or the item called "ABC Extended" (known as "US Extended" prior to OS X 10.11).

(The standard US layout does not use Option 6 for circumflex, it uses Option i. The US International PC layout uses Shift 6, while ABC Extended uses Option 6. I suspect you were using one of these layouts rather than "US".)