Absolutely not !
In any case, Apache would not have to pay Oracle, as it is the user of Java for JMeter (as for any other Java application) who would pay.
But, there is no such risk anyway.
JMeter needs Java >=8 (Java 9 and 10 are intermediate and not advised).
Java is provided by:
- Oracle
- Other vendors (IBM)
- OpenJDK
As of Java 8:
- Oracle is free
- OpenJDK is free
- IBM Java SDK is free
Only Oracle JDK >= 11 is subject to a paid support, OpenJDK is not.
And as you know there are already LTS (Long Term Support) free offers for jdk currently at least by Amazon and Redhat.
So no risk at all for Apache JMeter !
You can see that the jmeter github project runs on OpenJdk through TravisCI: