Yes, there aren't a huge number of employers. There are two kinds of employers: public and private. I've worked for both kinds (first San Zhong and now Chuang A), and they each have their advantages and disadvantages.
The public schools and universities: San Zhong, Yi Zhong (though they have an exclusive deal with an American company so you can't get a job there easily), Handan Engineering University all maintain a contingent of foreign teachers. Si Zhong occasionally has one, Er Zhong and Handan College I'm not sure. These places are relaxed, low-pay, low-hours, often with a very mediocre apartment provided for you (most often on-campus, which sucks). But you get a couple months holiday a year, which is great.
Private institutions: Lilac, Maple Leaf, Crazy English, Jinwutong, Chuang A. They're a mixed bag - Maple Leaf and (particularly) Lilac have a rotten reputation amongst the foreigners here for piling on unreasonable hours and being dodgy with pay. On the other hand, I had a friend at Jinwutong and he was very happy there, and I've only just started with Chuang A but so far they treat me very well. These places have fewer/no holidays, good pay, (generally) good apartment, more hours.
In the short time I've been here salaries are already a lot higher than they used to be. 4000RMB jobs exist alongside 10,000RMB jobs, so there's a big variety. Speaking Chinese is a HUGE asset if one wants to get the good positions.
Handan's economy is exploding, especially in the outskirt cities. So private teaching is a great money-maker in Handan. When I arrived the pay was rubbish, it was hard to get students even at 150 an hour, but nowadays foreigners aren't as numerous as before so you can get away with 200 or 250...even 300-500 if you have REALLY good guanxi. With the cost of living so low here, at one point I was saving about 120% of my salary (!) thanks to the extra work.
Aside from private tuition, many schools and kindergartens are eager to give you part-time work. Overall I recommend new arrivals in Handan go for low-pay, low-hours jobs with a relaxed employer (I'm told Maple Leaf regularly fires teachers for taking on extra work, but San Zhong and Chuang A turn a blind eye as long as it doesn't get in the way of your job). Then put yourself out there and pick up a few extra hours a week to really boost your salary, maintain flexible hours, and build up connections to get a better position when your contract expires.