Let's take a detailed look at French nasal vowels [these occur in a same syllable where the vowel is followed by either an "n" or "m"; when the soft palate drops letting vowel air go into and out the nasal structure]. I'm unsure what you mean by "bright" (as frequency strata or volume or something else) as regards it's relevance to these vowels.
The following graphs show the French non-nasal and nasal vowel formants. The formant "F0" is the fundamental acoustic resonance and are not here specially labelled, formant "Fr 1" starts under the line where appears annotated and is a widening of the frequency's bandwidth, and formant "Fr 2" starts under the libe where it appears annotated and is the last overtone of that vowel's vocal tract pitch resonance .
These graphs will cover the non-nasal and nasal vowels of "/a/", "/e/", "/o/", and the dual sound vowel "/oe/". The data is specific for what I consider representative of a podcast speaker's voice register (not excited dialogue) which is to say all data is for D4 (akin to "Re" of our common "Do-Re-Mi-Fa-Sol-Do" scale). D4's fundamental begins just under 300 Hz and that's around where these chart's formant "F0" start.
Note: in all comparisons the vowel chart on the left shown is of the non-nasal vowel and then on the right you will see the same vowel that is nasal. When comparatively among the non-nasal and same nasal vowel the colors are brighter that indicates frequencies with relatively greater power output. The bottom scale is in increments of seconds and the total time graphed is 2 seconds.
Here's "/a/" and nasal "/a/" [sorry graphs are odd sizes]:
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Comment : the non-nasal "/a/" has relatively more power around 300 Hz,
while the nasal "/a/" has relatively more power as the overtones rise. The cycling ups and downs of vocal vibrato over 2 seconds is essentially the same for both non-nasal and nasal "/a/".
Here's "/e/" and nasal "/e/":
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Comment: Although the non-nasal "/e/" frequency waves are generally brighter (more powerful) than the nasal "/e/" there are fewer of those brighter/powerful waves compared to the nasal "/e/" overtones in the Fr1 and Fr2 frequencies.
Here's "/o/"and nasal "/o/":
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Comment: around 2,000 Hz the non-nasal Fr2 overtones have less resonances than the similar nasal overtones until non-nasal Fr2 overtones return around 2,300 Hz and around 2,500 Hz the nasal overtones are less than the non-nasal.
Between 350 and 500 Hz there is less vocal tract vibrato of the non-nasal compared to the nasal.
Lastly here's "/oe/" and nasal "/oe/":
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Comment: the resonances are slightly affected in some of the fr1 frequencies which exhibit more power (as where seen brighter).