Apparently, fsolve has trouble with double integrals presented in the Int(..., [x= ..., y= ...]) form as opposed to the Int(Int(..., x= ...), y= ...) form.  Note the difference in the following two examples. 

restart:
J:= Int(a*x+y, [x= 0..1, y= 0..1]):
fsolve(J=0, a);
Error, (in fsolve) {x, y} are in the equation, and are not solved for

restart;
J:= Int(Int(a*x+y, x= 0..1), y= 0..1):
fsolve(J=0, a);
                          -1.000000000

Yet, for both forms type(J, freeof(x)) returns true. 

You can use the coeff command on either the series form or on the polynomial form that you had before converting it to a series.  If S is your series, then coeff(S,xi,0) and coeff(S,xi,2) will extract the expressions in your example.