It’d need to be 13 to 80 times more massive to be a brown dwarf.

https://en.m.wikipedia.org/wiki/Brown_dwarf

If it gained mass rapidly, most all the moons would likely destabilize since they’d have way too little velocity for the orbit they’d now be in. But if they sped up to accommodate, it’d depend on the density change of Jupiter. The fusion would push out material a bit, but the density would probably just increase because of the increased mass.

But if the density stayed the same, the radius would be 2.4 to 4.3 times larger than currently. With Jupiter having a radius of 70,000 km, that’d put it at 170,000 to 300,000 km radius. That’d put Metis and Adrastea inside 170, and Amalthea and Thebe inside 300. They’d already be heavily inside the jovian atmosphere, so they’d be toast. Io, Europa, and maybe others might also fall due to higher atmospheric drag at those levels.

https://en.m.wikipedia.org/wiki/Moons_of_Jupiter

I think the rest of the moons would be planets then, and the solar system would be a binary system.