That's true. Frankish custom was that the inheritance of a King should be split between his sons. That's one of the reasons Francia was splited in several kingdoms OTL, like Neustria or Austrasia. However, if there was only one son, then the Kingdom wouldn't be split.
Now, your Merovingian Kings were pretty "lucky" to only have one son as it went. If you plan to change that in the future, I fear you will need to change the Successoral Law. Another possibility would be that Royal Authority collapsed like it did OTL : the Mayors of the Palace became then de facto rulers, with one Frankish King to rule the whole kingdom as their puppet.