Depending on your needs, either Scribus or Inkscape would be good choices. Both are Free / Open Source software and both are available in a variety of languages. If you are looking for great software to use for a long time, I highly recommend these two. I am an ESL teacher and use both at least once or twice a week.
Inkscape is good for graphics and individual worksheets. It uses SVG format, which allows the results to be scaled to pretty much any size without loss of quality. You can quickly create quality, good-looking worksheets, export to PDF and print. Inkscape can also export to common image formats such as PNG and JPG. You can find lots of useful SVG files (maps, flags, icons, etc.) on Wikipedia or the associated site wikimedia.
Scribus is much more complex and, I think, much more powerful. It is desktop publishing software, so is great for multi-page documents that include (for example) linked text boxes and graphics. You can even create PDF forms with it, although it doesn't sound like you would need that feature.
Just wanted to mention that I've found this book really helpful for learning the details of English teaching in various countries.
There's this phonics karuta: https://www.amazon.co.jp/gp/product/4828864741
It's pretty expensive considering, but it basically has words on one side, and pictures on the other side.
You could make something similar.
Example (for F and "magic E"):
F - F - FISH
F - F - FROG
FI - FI - FISH
FI - FI - FINE
If you want a picture of the actual phonics karuta, send me a message, and I'll send you a picture of some of the cards and the instructions (they're in Japanese, though...)