Learn French: Mon sac est plein.

In this sentence, plein is used as a regular adjective meaning 'full' (describing the state of the bag). However, it is a great connection to make! In spoken French, you will often hear the phrase plein de, which works exactly like beaucoup de to mean 'a lot of' or 'plenty of'. For example, Il y a plein de sacs means 'There are lots of bags'.

Would plein change if the object was feminine?

Yes! Because sac is masculine, we use the masculine adjective plein. If you were talking about a feminine object, like a suitcase (une valise), you would add an -e to make it feminine: Ma valise est pleine. Adding the -e also changes the pronunciation so you can clearly hear the 'n' sound at the end.

As a quick refresher, do I use mon here because the speaker is male?

No, you use mon because the object you own (le sac) is masculine. In French, possessive words like 'my' (mon, ma, mes) always match the gender of the thing being owned, not the person who owns it. So, both a man and a woman will always say mon sac.