In the UK on visa-free entry, can I visit Europe and return?

You are a US national who entered the UK under Paragraph 23A of the Immigration Rules...

A person who is not a visa national and who is seeking leave to enter on arrival in the United Kingdom for a period not exceeding 6 months for a purpose for which prior entry clearance is not required under these Rules may be granted such leave, for a period not exceeding 6 months.

(or in plain English, you got stamped in for 6 months at the airport when you arrived). I don't know what you told the IO in your landing interview but I assume you did not indicate your intent to stay for the full 6 months (or you probably wouldn't be asking the question you did).

And now you want to make a short visit to France and want to know...

I'm just wondering whether there will be an issue getting back into the UK after I leave for a few days?

So we turn to Paragraph 20A of the rules, which says in part...

Leave to enter or remain in the United Kingdom will usually lapse on the holder going to a country or territory outside the common travel area. However, under article 13 of the Immigration (Leave to Enter and Remain) Order 2000 such leave will not lapse where it was given for a period exceeding six months or where it was conferred by means of an entry clearance (other than a visit visa).

What it means in your case is your 6 month stamp will be 'used up' the moment you leave the common travel area (the CTA does not include France). So your leave to enter will expire and any unspent leave will be forfeit. Long story short, you cannot return with the stamp you got last May.

So that puts everything back to Paragraph 23A all over again! You'll have a landing interview just like last May, except presumably it will be at the juxtaposed controls in Calais. And the big difference is that the IO will see that you have been here for 4 or 5 months and wonder how you described the purpose of your visit in your previous landing interview. On the one hand it could be awkward and on the other hand people use that strategy all the time.

The 'gamble' that people take is expressed in V 4.2 (b)...

...will not live in the UK for extended periods through frequent or successive visits, or make the UK their main home;

The Immigration Officer makes the determination based on the evidence he obtains during the landing interview (and subsequent inspection if he thinks it's necessary).

If things go well, you will get stamped in for a brand new 6 months starting on the date you arrive in Dover (that's the carrot and why people try it). If things go mediocre they will keep your passport and tell you to collect it at the airport in 7 days time (a temporary admission). And if things go really bad, you will be served removal papers and bounced (most likely to France). Nobody can predict the outcome in these things because it's all down to personal impact and articulation skills on your part.

So the absolute answer to your question 'will there be an issue' is indeterminate and not something the internet can provide. Some win, some lose.

The rules I cited from are here. But they are also put forward in easier language in Appendix V.