Was the bike you tested a 54 or a 57?
The truth is, there is little difference in geometry between men's and womens when you factor in stack (overall height of the front end), reach (arm length/arm room) horizontal top tube (cockpit length, more or less) and head tube angle (which is a function of the others, or maybe vice versa). Maybe an equivalent mens version is perhaps a centimeter longer, but the stem length (thing that attaches the bars to the bike) can be changed to accommodate small differences in size. Depending on a particular bike's geometry, a mens bike may actually be a little smaller, rather than the womens. Geometries are not standard between brands, models within brands, or even in the same model, as they change from year to year.
A men's Secteur is definitely worth trying to give yourself more options.
Reach: this number basically denotes arm room. If you have long arms, too, (like me), then you might need a bike with a longer reach to allow them to fit. In fact, it sounded from your description that the reach was too short, but if it was a size 54, then the entire bike was too small, so not sure.
Verdict. At your height, there are a lot of options. Don't limit yourself to women's.
Also, look into a Giant Defy, as well. They are available at a range of prices, starting at less than 700 dollars.
Another consideration: it is likely you will eventually decide to upgrade to a more expensive bike, or maybe just a more aggressive bike (suitable for someone who has been riding for a few years). At that point, you may decide to sell. Men's bikes are easier to sell than women's and tend to be worth more money on the used market. Especially one for a 5'10" rider. If you get a good deal on whatever bike you buy, it is possible to get a good return. And speaking of, keep all original parts, that way, any upgrades you make you can keep and transfer to a new future bike, and put the original stock (cheap) parts on the old bike to sell. JMTC.