  Marx (STOC~2010, J.~ACM 2013) introduced the notion of submodular width of a
conjunctive query (CQ) and showed that for any class $\Phi$ of Boolean CQs of
bounded submodular width, the model-checking problem for $\Phi$ on the class of
all finite structures is fixed-parameter tractable (FPT). Note that for
non-Boolean queries, the size of the query result may be far too large to be
computed entirely within FPT time. We investigate the free-connex variant of
submodular width and generalise Marx's result to non-Boolean queries as
follows: For every class $\Phi$ of CQs of bounded free-connex submodular width,
within FPT-preprocessing time we can build a data structure that allows to
enumerate, without repetition and with constant delay, all tuples of the query
result. Our proof builds upon Marx's splitting routine to decompose the query
result into a union of results; but we have to tackle the additional technical
difficulty to ensure that these can be enumerated efficiently.
