By default, Illustrator, Photoshop and other apps automatically switch to a default font whenever you type a character that’s missing from the current font.
This occurs with missing capitals/lowercase letters or accented characters (diacritics) - even if they are in the font - as you enter several character keys to type them.
For instance, to enter the character é (small letter e with acute) you might first press the acute accent ´ and then the lowercase e. If you font does not include the acute accent ´ as a separate glyph, the app will switch to the default font and your accented character é will not be displayed with your font :(
Hopefully you can solve this in a couple ways:
In Adobe apps, disable the substitution by unchecking Preferences > Type > Enable Missing Glyph Protection
If you want to keep substitutions enabled, you can also simply select the accented character and reassign your font from the Character Panel ;)
Create new glyphs for each accent so your font contains a character for each of the diacritical marks, like the acute accent ´ (you will find the most common ones in the Font Template from the top right menu).