Speaking is mostly muscle memory, so any slight change to the shape and location of your teeth is likely to cause a little bit of a disruption in how you talk. As you can imagine, this is going to be the case when you first get your dentures.
It may take some time to get used to speaking with your dentures in, but practice makes perfect in this regard. Find time to work on speaking slowly, getting used to how it feels to have your prosthetic in as you do so. You might try reading aloud for a while or conversing with someone you trust until talking feels natural again.