I love Myra Jean! I think in most cases, names that end in vowels (or vowel sounds) go best with middle names that begin with consonants, and vice versa. That being said, here are some suggestions:

Myra Beatrice (I personally prefer this to Myra Bea)

Myra Charlotte

Myra Caroline 

Myra Catherine

Myra Dorothy 

Myra Florence 

Myra Frances

Myra Helen 

Myra June 

Myra Jane 

Myra Josephine 

Myra louise

Myra Lillian/ Myra Lily

Myra Louise/Louisa

Myra Phoebe

Myra Sophie

Myra Vivian  

I guess the main question I would ask is, are you deliberately going for a retro sound? Myra peaked in the 1930s and 40s, and while I do like it, I think it might still sound like an old lady name to a lot of people. Middles that are also dated, like Jean, Estelle and to a slightly lesser extent, Bea, will just emphasize that feeling. Myra Jean in particular sounds to me like a lady in her seventies or early eighties who might be old school friends with my grandmother (other ladies in their circle: Wilma, Phyllis, Doris and Geraldine). This isn't a criticism—if you like that style, awesome. I personally would choose to go with a more current, youthful middle to balance out the old lady associations. I think that Myra Delphine, Myra Eloise and Myra Evangeline work really nicely for that. 

In terms of other suggestions, you seem to like French names. How about: Myra Genevieve, Myra Vivienne, Myra Corinne, Myra Camille, Myra Blanche, Myra Coralie, Myra Natalie, Myra Gabrielle, Myra Catherine, Myra Sylvie.

My favorite is Myra Jean.  

Evangeline is a nice name, but seems a little too flowery next to Myra.  I think I'd prefer the simpler Myra Eve.  If you prefer something longer/more flowery then something like Myra Genevieve keeps some of the feel of Evangeline, but I think has a better flow.

Myra Estelle is also very nice.

Some other suggestions, Cordelia, Jane, Helen, Corinne, Claire, Agnes, Dorothy

I like Myra Jean best, and also like the suggestion of Myra Catherine.

I work with a Myra in her '60s so I agree with EVie on that topic.  I prefer a middle that is longer and ends with a consonant sound to go with it, so my favorite on your list is Myra Evangeline. 

Other Ideas: I also like Myra Genevieve and Myra Vivian/Vivienne but my favorite is Myra Juliette.  Something a little more unusual like Myra Avalon or even Myra Avonlea could also work.