The espresso blends I like tend to emphasize the chocolate, nutty, caramel flavors e.g. Vivace, Velton's Bonsai, Counter Culture's Toscana, Red Bird, Klatch Belle. I don't really like the overly sour, citrus fruit flavors. Single origins in espresso are not really my bag.

I'm giving espresso a break and experimenting with French press. What happens to the flavor profiles of espresso blends brewed using French press?

Or should I be trying different types of coffees to get the best out of the French press process?

You can use whatever you like to brew any method.

Generally it used to go, espresso intended coffee makes good brewed coffee, brewed coffee intended coffee doesnt make good espresso.

But, since people these days, some of them anyway, like really bright acidic espresso, thats not always true anymore.

Blends like you mentioned will do fine in any brew method. You generally will find them less intense, but should have similar flavor profiles for the most part. I used to really like espresso blends as brewed coffee, but my tastes for brewed coffee have gravitated to those brighter, acidic more fruity coffees as well, so I dont use espresso purposed coffees for brewing as much these days.

That said, if I was out of my usual single origins for brewing, and I wanted some pour over or whatever, I would not hesitate to grab whatever I was using for espresso at that moment, and brew it up.

Because espresso extraction is such torture to the coffee, there is a little less leeway in what coffee you can use. Assuming its roasted with at least some competency, pretty much any coffee will taste good brewed. And, a lot of times.. much better than just "good".

Brew it up, see how you like it. I can vouch for Belle, Toscano and Redbird all making decent, chocolately brewed coffee. Belle especially, as there is some berries or cherry like fruit going on.

When I roast for pour over, I like snappy fruity quick roasts. In espresso this tastes slightly tart/slightly sour. So I stretch out the roast slightly for espresso to get more balance and depth in the cup. I don't really know how many others still really use this approach, but I think any well roasted coffee, wether for espresso or not should be great in a french press

For these blends in French Press, try grinding a little coarser than you would for roasts intended for brewing only.

Not all single origins are " sour and citrus ...." thats a fairly broad brush to characterise all coffee with, perhaps you haven't found a single origin you like for espresso or perhaps your just under extracting the ones your tried...you can have a nice sweet balanced citrus espresso....
Anyway Perhaps look for a good quality brazillian single origin for brewed , to deliver a nice sweet balanced cup with choc, caramel and nuts notes...this may be more what you are looking for in a coffee and certainly achievable with the right single origin

The blend I roast for espresso is one of my wife's favorite in the french press. Like mentioned earlier, it is tailored to make a good balanced shot, however it seems like a nice mild somewhat toned down version of what the same blend tastes like if roasted lighter and a bit faster. I would prefer the non-espresso roast of this blend if it were up to me, but the wife does not like overly bright coffee, so the longer darker roast which makes it so good for espresso, also suits her taste in the press. That's a win for me. I can roast SO's or blends for press that I like, and then just up the amount I already roast for espresso so that she can also use it in the press.