My suspicion is that you have not bought an RGB modded NES, but a plain original french NES. The french NES has an internal convertor (instead of RF box), creating an ”RGB” signal from composite video. I.e. it’s not proper RGB. I have no idea what are the specs for voltages of this signal, in theory it should still work with the OSSC, obviously in your case it doesn’t. Although it detects the sync, the signal is 50Hz as expected.
(Edit: It’s also possible the signal is valid but your TVs don’t support 50Hz over HDMI.)
You can read a bit more about it here: http://blog.hardcoregaming101.net/2009/12/french-nes-with-rgb-output.html
I would re-sell or return the item and get a proper NTSC RGB modded NES. Optionally you could swap the innards for a 60Hz RGB modded mobo, but maybe it would be a shame considering the french model is quite unique and potentially a collectors item.