Try:

Times @@ (a + b + c)

Apply and Plus have different precedences:

In[1]:= Precedence[Apply]
Out[1]= 620.

In[2]:= Precedence[Plus]
Out[2]= 310.

The higher the precedence, the tighter it will bind a function/argument pair. This matters only when using infix notation. Bracketing overrides the precedence pairings.

Prefix notation is not affected by precedences, since the syntax itself decides order of evaluation:

Apply[Times, Plus[a, b, c]]

Postfix notation also generally works Ok:

a + b + c // Times @@ # &

Times @@ a + b + c

is the same as

(Times @@ a) + b + c

and

Times @@ a

is just a.