Can the average Haitian understand French?
If I had to answer this question in a single word, then the answer is "NO".
But to get down to the nitty gritty, which average Haitian are you talking about?
If you have a sense for Haiti's literacy statistics (slightly over 50%), and the challenges regarding access to education that have characterized Haiti's history, then you may get a pretty accurate picture for the number of Haitians who actually do speak and understand French fluenty; they are a minority, and come either from a privileged elite, or from a middle class that has expanded over the years, but still represents a small percentage of Haitians. French in Haiti is only learned in school and in church; the Haitians that speak French at home are few and far between.
Regarding comparisons of French and Creole, here's the deal:
The majority of the Haitian Creole lexicon comes directly from French, and mostly old French (which is why sometimes there more similarities between Creole and Quebecois French vs. European French). This French lexicon enables French speakers with a sharp ear to pick up many terms in Haitian expressions, and rarely, to garner meaning. But otherwise, these are two different languages.
Haitian Creole has a completely different grammar and syntax; for example, definite articles follow nouns instead of preceding them, and they do not have any gender assignment.
French: le chien
Creole: chen la
French: la boite
Creole: bwat la
Conjugation is totally different.
French: J'ai, tu as, il/elle a, nous avons, vous avez, ils/elles ont
Creole: Mwen genyen, Ou genyen, li/li genyen, nou genyen, nou genyen, yo/yo genyen
(Note, there is no difference between "he" and "she" in Creole, nor any difference between "we" and "you - plural"; these details are determined by context)
(Note, there is no difference in creole between the infinitive form of a verb, and the conjugated form)
(Note, the Creole etymology of "genyen" as "to have" is unknown to me, but it may come from "gagner")
Conjugations in the past and future are not performed by changing the root verb; they are formed by adding terms.
J'ai eu = Mwen te genyen
J'avais = Mwen te konn genyen
J'aurai = Mwen pral genyen
Another barrier to clean translation between Creole and French is the Vodou culture - it is intrinsically bound up in the Creole language such that even if French terms are used in some expressions, their provenance gives them a subtle, or sometimes grossly different meaning.
Example: Someone walks into a home and Says "Hone" prounced 'O-NEH' (French = Honneur)
Proper response "Respe" pronounced 'RAY-SPEH' (French = Respect)
Probably not much meaning in French. RICH with meaning in Creole.
I won't keep going unless you have specific questions or requests for more examples - but these are some examples to demonstrate that Haitian Creole is not at all "broken French" - it is an altogether different language with significant French influence.
Other linguistic influences on creole include a number of African languages, Portuguese, Spanish and English.
It is possible, however, for the MOST RUDIMENTARY interactions in both French and Creole to be mutually understandable - but some luck is involved. Many greetings, all numbers, and some basic elements of everyday life are basically the same in both languages - air, water, bathroom, food... these all share similar terms.
This is a volunteer program. None of the attorneys (like me) are getting paid. Do you want to volunteer your interpreting services?