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).
Other reasons
If the accents still do not show up despite being created, check these reasons: