The French et al early on signaled they favored letting the IDF act and have recently backed off. The change is because the IDF acted slower, with more deliberation than anticipated. The current action is a holding scenario to allow the war to proceed.
When the IDF is deemed successful or it seems a success, the malleable positions will revert to that near the beginning.
I am convinced that a fighting force led by France and involving the Lebanese Army will ultimately occupy the south. There will be others but France will lead. I enjoy Frog bashing as well as anybody, but they are the only logical nation for the job.