Paris Saint Germain, Monaco and Brest will represent Ligue 1 in the Champions League next season. By changing the format of the Champions League to a new format, Ligue 1 will get 1 additional slot for the team that will compete in the Champions League. However, I don't see them being able to compete there, because it is a difficult place, only Paris Saint Germain will probably be able to go further and even then they will still fail to win the title they have always wanted.
Compared to teams from other leagues, I don't see them being more convincing, because the competition in Ligue 1 itself doesn't have a good competitive level, so that will affect their performance in bigger competitions. Apart from that, in my opinion their mentality is no better than other league teams. I don't mean to underestimate them, but this is my assessment of several teams that will be in the Champions League representing Ligue 1.
Ligue 1 is just a way for PSG to play in the Champions League so far, because there is no competition which puts them at risk of failing to win in Ligue 1 or missing the Champions League next season, currently Ligue 1 is sending more representatives for play in champions league next season, but even so, it looks like they won't be able to get out of the semi league phase later, currently the teams in Ligue 1 are not strong enough teams and even in the domestic league they are not able to compete with PSG, so there is no reason for us to see that Brest and Monaco are able to compete with other strong European teams in champions league.
PSG is the only strong team that Ligue 1 has in the Champions League, but even so, their it is still doubtful that they will be able to compete for the title in the Champions League, let alone other Ligue 1 teams? currently, Ligue 1 is the least competitive league in Europe so indeed this makes the mentality of the teams in Ligue 1 very weak, we can even see how great PSG in Ligue 1, but because their mentality has not been tested by the tight competition in the league, of course they often lose mentally when facing other teams in the champions league so far.