Yes this seems to be true for now. However keep in mind, that the hot months are just beginning and have a high impact on the energy production of France.

Here are charts I found. They are a bit difficult to read: Basically the width of the connection on a country determines the amount of energy they sent over the connection. So the connection from France to Switzerland which is much broader on the FR side says France exports more than it imports from Switzerland. For Spains the reverse is true as the connection is broader on the ES side.

To see the impact of hot months compare the charts for May and July-September of last year.

I think France will in average stay a net exporter for the next years, but in the trend they will shift to more importing as many of their nuclear reactors need maintenance or replacement and all of them are affected by climate change. The trend may of course change again due to changes in politics.

Not really

~~That is true.~~ [Édith: apparently not!‽]

However, import/export stats usually just show where energy is cheapest. Of course it's cheaper to use French excess nuclear energy than start a German gas/coal plant. Germany has more than enough (fossil) capacity on its own, however.

The 2022 situation in France is an outlier in this regard obviously, because it temporarily reduced French generation capacity below their needs. Also outliers: Countries like Italy and Hungary that never had enough generation capacity in the first place and do need to import rather than importing to reduce cost.