AFAIK, no modern language is close enough to latin to help communicate directly. I think some of the romance languages, maybe even most, are close enough to speed the learning process quite a lot, but the pronunciation, vocabulary, and even grammar have shifted quite a lot. It has been almost two millennia and quite a lot change has happened.
Similarly knowing greek modern or classical would probably help, since most educated romans IIRC could understand greek. Unfortunately they probably knew the contemporary version of greek which is different from either modern or classical versions.
I expect latin would be difficult to learn for someone whose native tongue is english and does not know any romance languages. Fortunately it is simple to justify american knowing spanish, french, or portuguese.
I think the common solution is to assume that whatever implausible mechanism allows time travel also gives the language. This is actually reasonable for some methods.
The hard core solution is simply to give the time traveler the time to learn. If he can prove he is literate, has some modern technology, such as say a printed book (printing and paper), and is very lucky where he lands he might be given the time and opportunity to learn the language.
Alternately you might give him time to prepare for the trip in advance. It is still fairly easy to learn classical latin (or greek), vulgar latin might be more difficult.
Or if you really just need an excuse, a father who was a latinist and insisted using latin in normal discussion will be good enough to get some basic phrases and a huge head start in understanding what people say.
Jimmy360 has a very good point with pointing out latin is taught at school. Sometimes the simplest solution is the best. Learning latin is much less common than it used to be, but it is not like it is somehow more implausible than, to pick an entirely random example, time travel. When you get right down to it, from storytelling perspective it would be nice to have some link that makes it so that just this person travels in time and just to that particular time and place. Invert the problem from plausibility of time traveler learning latin to plausibility of latinist traveling in time.
You have to think some reason for the time travel anyway, so this reduces your issues from two to one.