What is that format and are there some online tools I can use for this?
The format as already mentioned is called "Red Book" or "CD-Audio".
It is not a file format, or even a filesystem format like UDF or ISO9660 are – better think of it as an entirely different class of CD contents than a "data" CD.
Can I just use Fre:AC for converting the MP3 files into CD format and copy that on the CD, using simple copy-paste or am I missing something?
No. In the original audio CD format (Red Book), the tracks are not files. Such a CD has no filesystem at all, only a Table of Contents describing ranges of raw audio data sectors.
In other words, the audio is stored alongside any 'data' track, not within it. Indeed standard audio CDs, the kind you're looking for, really have no 'data' track at all.
(Mixed-mode CDs are uncommon, but imagining the track structure of one – with multiple audio tracks adjacent to a data track – might aid understanding. Maybe a close analogy would be if an HDD's partition table had a separate partition for each audio track, and that track .wav was dd-copied into its dedicated partition.)
Except there's still more to it – for example, "closing" each track is done by sending a specific SCSI command to the CD burner device, not merely by writing ordinary data.
So an online conversion tool could give you files in the correct format (which is just plain uncompressed PCM, like in typical .wav files) but it could not build the entire track structure. Even if the online tool provides an "image" in .cue/.bin/.wav format, it would still need to be written using a specific tool that understands .cue and knows how to write each of the multiple tracks – and those are actually harder to find than "regular" audio CD burning tools.
There are many programs which can burn an audio CD from a bunch of MP3s. Many music players (e.g. iTunes or Windows Media Player) still have, or used to have, that capability. Among dedicated tools, CDBurnerXP is capable of doing so. If you're running Linux, K3b used to be popular.
All such tools will automatically convert your audio files into the correct format (44.1kHz PCM) as part of the process, so usually you can just drop an MP3 into the list.
In all cases, though, it is a whole dedicated mode and not a specific type of file or filesystem "formatting". (For example, note how the K3b screenshot has a flat list of tracks, without any folders.)
Finally – keep in mind that some very old CD players were unable to read a CD-RW, so if your player was bought in early 1990s, it might be necessary to use a CD-R specifically.