What you need to know:
Length - The Map says 4.2 but is closer to 5.4
Water - french creek is a reliable source plus numerous other small creeks along the way.
Water crossings - french creek twice, can be difficult depending on the amount of rainfall. plus several other small creeks.
Camping - Camping within custer state park is only allowed at designated campsites or within the french creek natural area. So you can camp within the french creek natural area where there is a$7 per night fee or continue a mile past the badger hole trail head and camp at legion lake. i would call ahead and make sure there are spots available at legion lake before starting out.
wildlife - buffalo on the trail are likely. Pronghorn antelope. elk can been seen but are rare.
Trail condition - The trail is well defined and easy to follow. there are several steep and rocky climbs. french creek can be a tricky crossing if the water levels are high.
Helpful info - some gpx tracks show the trail as being farther west than it actually is on the northern half of this section, so just stay on the trail and you’ll be OK.
also, the badger hole trail head is a 1/4 mile side trail. if you are through hiking and don’t need to go to legion lake for anything, continue north at the marked intersection. keep in mind that the main centennial trail does not have access to legion lake so if you need to go to legion lake for water, supplies or camping, you will want to take the side trail to the badger hole trail head. from there it is another .3 miles to the legion lake store, restaurant and campground. this trail is mostly a small road but is not well marked, so i included a gpx track below.