Thanks to some friends who have given me feedback in both blog comments and e-mails, I've learned that the one browser that doesn't display the French accented characters in my blog is Safari on the Macintosh.
I can enter the accents as HTML codes in my text, but I'm not inclined to do so. Typing them the way I do is easy and quick. Writing the blog is not a professional enterprise. I'm not selling anything.
I can also quit using the French accented characters. Ha! No way, José.
If you are using the Safari browser on a Mac, here's a work-around (as they say in the software business): use Firefox instead. Firefox is a free download here. Choose the language you want and the operating system you use (Mac, in this case). I've been using Firefox on Windows for a while now, and I like it.
Want to see what the HTML codes for accented characters look like? Here's the code for an e with an accute accent: & # 2 3 3 ; I would have to type that without the spaces between the characters for you to see this character: é. So the word café would look like this in my text, without the spaces between the characters: c a f & # 2 3 3 ;. That would make proofreading impossible.
Maybe there's a side of this I haven't figured out yet. I have to deal with the Blogger editing application too. For now, I'm not going to change anything.