There is generally a negative correlation between a currency and its home stock market. So you might expect GBP to be rising if the FTSE100 is falling, and GBP to be falling if the FTSE100 is rising.
Same for USD and the Dow. Etc. etc.
But its a very loose correlation, so many times you can see both rising or both falling. The rule is not accurate and dependable enough for a trade decision. It might help as a filter or as a sense-check before you pull the trigger.
Its very difficult to predict how news affects a pair, even if it is straightforwardly and strongly positive or negative for one of the currencies. Even many experienced traders don’t even attempt this, they avoid holding relevant (or any) positions across important news announcements.