I have an installation that has three potentially high-power aspects to it:
a water pump that can technically draw 8A but that I have never seen draw more than 1.5A. This will be on for perhaps a half hour every day between April and September. Typically during hours where the solar cells will be active.
some LED arrays that consume between them about 3W @12V. These are attached to motion sensors so usage is difficult to assess. Perhaps 15 mins every 24 hours
a SIM900 module. Technically this can draw up to 3A. I have never seen it take more than 200mA. Usage is dependent, but possibly 1 minute per day.
The rest of the circuitry is at the microAmp level.
So it seems that the possible energy usage is about 1Ah.
the installation will be powered by an old 12V 60Ah car battery (sealed)
to save costs (this is largely an upcycling project) I'd like to avoid a charge controller.
the solar install will be in the South of France (the Gers). So between 6 and 9 sun-hours per day between April and September.
This suggests that I should be able to "get away with" a solar panel of 5W. is that correct? I can't help feeling I've screwed up my maths somewhere ....
You need to actually measure the current draw, especially the peak. "I have never seen draw more than 1.5A" -- you obviously haven't looked carefully. Motors briefly draw the stall current every time they start up. Likewise, phone modules consume 1-2 amperes while transmitting.
After having measured the current draw, plan for the total number of hours of operation to get ampere-hours per day. Check local tables of sunlight hours to get the hours of useful operation of the solar panel per day. The panel should probably provide at least twice the required ampere hours.
How is your system expected to operate during a two-week cloudy period?
This JRC website is useful for estimating the available solar energy at your location.
However the big challenge will be estimating the worst-case situation where there may be a prolonged spell of cloudy weather during the shorter winter days.
I reckon you should do the calculations @jremington has suggested and be prepared to double the size of your solar panel if the initial estimate proves to be inadequate.
You also need to build into your calculations the need to avoid the battery remaining at a low charge level for a prolonged period - that will ruin them very quickly. It should really get a very full charge at least once per week.
And be aware that car starter batteries are not designed to be deep-discharged. They are designed to provide a high current for a few seconds to start the engine and then be recharged again immediately.