The river can be expected to move towards Louisiana's Atchafalaya River, according to this post,.
"On this map, each is at the approximate height of a typical spring flow. At top center, we see the Old River Control system and its branching east-west connector channel. The gap in the linear levee west and just before the last turn of the Mississippi is the Morganza Spillway.
At equal latitude, the Mississippi runs across a narrow terrace of land, much higher than the neighboring Atchafalaya. In many spots, at flood stage, a single levee appears to be the only barrier between the two – a fact that should have even the most Katrina-jaded New Orleanian sweating beads."