If this is about connecting the color computer to television antenna input via an RF modulator, then the local TV system variant matters, as both the RF modulator for the computer and the RF demodulator in the TV are built to use a certain composite video signal bandwidth.
For a 625-line 50 Hz field rate TV system, the maximum composite video signal bandwidth ever used with PAL or SECAM color encoding over RF is 6 MHz.
As the line rate of a 625/50 TV system is 15625 Hz, it means that 384 cycles of 6 MHz sine wave fits into one line. As one cycle of sine wave means basically a white pixel and a black pixel, there are 768 total pixels per line, with a pixel clock of 12 MHz. Since the active video portion of a line is 52us out of the 64us, there are 624 active pixels, of which not all are even visible due to the TV image being slightly overscanned.
In practice, if direct composite video connection is used, the RF modulation and demodulation are not present to artificially limit the bandwidth to 6 MHz.
Basically this means that the situation is similar than between equipment in a TV studio, the transmitting device like a camera can use as much as bandwidth as it can and the receiving device can use as much bandwidth as it possibly can. There is a good chance that consumer TV equipment can have similar bandwidth limitations on the composite input than on the RF input, but it can also accept higher bandwidth.
There is not much use going past 6 MHz though, as even the BT.601 standard digital component video used in studios does not use analogue bandwidth much past 6 MHz, but it samples the PAL and SECAM signals at 13.5 MHz to arrive at 702 active pixels for the analogue portion of the line, so that sets the point of having overkill resolution.
So having said that, I would estimate that due to 5% of overscan per side, and the requirement to fit text well inside the edges of a TV, the usable area would be maybe 90% of the 624 pixels or 562 pixels tops. In worst case if you lived in a country with a 5 MHz TV system with bandwidth for 520 pixels, maybe less than 470 pixels per line via the RF modulator. With direct composite video connection, maybe 640 usable pixels per line is achievable as a practical maximum, but it can already be blurry and sharp edges will have fringe colors. 640 pixels would achieve 80 colums with a font of 8 pixels wide.
For vertical resolution, the PAL signal has 576 active lines when interlaced, or 288 active lines per field. Accounting for the overscan, there would be about 256 lines visible per field, or 512 lines per interlaced frame.
So through this thought process, I ended up with a resolution of 640x512 as the resolution that is the approximate maximum that can still be presented on a TV without too much blurring.
If we compare this to for example an Amiga 1000 which was designed in the early 80s, it also happens to use 640x512 as the hi-res mode. It also allows individually to halve the horizontal resolution by two to have a lo-res mode with 320 pixels per line, and it also allows turning off the interlacing to have a progressive mode with 256 lines per frame.
In real life, it is a bit more complex than that, since while the composite video signal can have bandwidth up to 6 MHz, it only applies to the monochrome brightness signal, the color resolution is much less as it only has a bandwidth of 1.3 MHz.