In the context of memes, you will say something like “quand j’évite les problèmes”. Here, the adverb “quand” highlights the same idea of an action as the BE-ing present.

Here is an example:

“Quand j’apprends que la fête est annulée”

If you’re also using this form instead of the longer “that’s me doing X” while showing pictures to friends and relatives you’ll find that the following forms are very often used; you can also use these forms in various ways as for instance in a humourous way or a sarcastic fashion when you draw a comparison between yourself and a personnage (real life character or played character) or entity of any sort (Mickey Mouse, a monkey, a martian, …) that you see in a paper, on TV, on film in general, in a painting, or even as a statue.

• Moi en train de X     Moi en train de lire le journal
• Moi à X    à la batterie, à la vaisselle, … (“à la vaisselle” might be at the limit of what is acceptable. (see commments))
• Moi devant X    Moi devant le café de la gare, …
• Moi sur …, sous …, … (There is no end of the prépositions and forms you can use here.)

You can replace “Moi” with “C’est moi” or “Me voilà“; if you want to make a transition from one picture to the next, you can add “Là c’est” or “Ça c’est” in front of “Moi” (Là c’est moi …).

In most
of these forms and contexts you can change “moi “with “toi”, “vous”, “lui”, “elle” and “eux”, and thus, instead of pointing at yourself, make someone else the subject of your remark.